--- _id: '14930' abstract: - lang: eng text: In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable locally free representations of fixed rank is independent of the orientation of Q. We also prove that the number of isomorphism classes of locally free absolutely indecomposable representations of the preprojective algebra of Q over R equals the number of isomorphism classes of locally free absolutely indecomposable representations of Q over R[t]/(t2). Using these results together with results of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification of pairs (Q, R) such that the set of isomorphism classes of indecomposable locally free representations of Q over R is finite. Finally when the representation is free of rank 1 at each vertex of Q, we study the function that counts the number of isomorphism classes of absolutely indecomposable locally free representations of Q over the Frobenius algebra Fq[t]/(tr). We prove that they are polynomial in q and their generating function is rational and satisfies a functional equation. acknowledgement: Special thanks go to Christof Geiss, Bernard Leclerc and Jan Schröer for explaining their work but also for sharing some unpublished results with us. We also thank the referee for many useful suggestions. We would like to thank Tommaso Scognamiglio for pointing out a mistake in the proof of Proposition 5.17 in an earlier version of the paper. We would like also to thank Alexander Beilinson, Bill Crawley-Boevey, Joel Kamnitzer, and Peng Shan for useful discussions. article_number: '20' article_processing_charge: No article_type: original author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Emmanuel full_name: Letellier, Emmanuel last_name: Letellier - first_name: Fernando full_name: Rodriguez-Villegas, Fernando last_name: Rodriguez-Villegas citation: ama: Hausel T, Letellier E, Rodriguez-Villegas F. Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. 2024;30(2). doi:10.1007/s00029-023-00914-2 apa: Hausel, T., Letellier, E., & Rodriguez-Villegas, F. (2024). Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. Springer Nature. https://doi.org/10.1007/s00029-023-00914-2 chicago: Hausel, Tamás, Emmanuel Letellier, and Fernando Rodriguez-Villegas. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” Selecta Mathematica. Springer Nature, 2024. https://doi.org/10.1007/s00029-023-00914-2. ieee: T. Hausel, E. Letellier, and F. Rodriguez-Villegas, “Locally free representations of quivers over commutative Frobenius algebras,” Selecta Mathematica, vol. 30, no. 2. Springer Nature, 2024. ista: Hausel T, Letellier E, Rodriguez-Villegas F. 2024. Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. 30(2), 20. mla: Hausel, Tamás, et al. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” Selecta Mathematica, vol. 30, no. 2, 20, Springer Nature, 2024, doi:10.1007/s00029-023-00914-2. short: T. Hausel, E. Letellier, F. Rodriguez-Villegas, Selecta Mathematica 30 (2024). date_created: 2024-02-04T23:00:53Z date_published: 2024-01-27T00:00:00Z date_updated: 2024-02-05T12:58:21Z day: '27' department: - _id: TaHa doi: 10.1007/s00029-023-00914-2 intvolume: ' 30' issue: '2' language: - iso: eng month: '01' oa_version: None publication: Selecta Mathematica publication_identifier: eissn: - 1420-9020 issn: - 1022-1824 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Locally free representations of quivers over commutative Frobenius algebras type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2024' ... --- _id: '14986' abstract: - lang: eng text: We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k). Let k be an algebraically closed field of characteristic p>n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod) of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman to the tamely ramified case. We also prove a correspondence between flat connections on X with regular singularities and meromorphic Higgs bundles on the Frobenius twist X(1) of X with first order poles . acknowledgement: "This work was supported by the NSF [DMS-1502125to S.S.]; and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement [101034413 to S.S.].\r\nI would like to thank my advisor Tom Nevins for many helpful discussions on this subject and for his comments on this paper. I would like to thank Christopher Dodd, Michael Groechenig, and Tamas Hausel for helpful conversations. I would like to thank Tsao-Hsien Chen for useful comments on an earlier version of this paper." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Shiyu full_name: Shen, Shiyu id: 544cccd3-9005-11ec-87bc-94aef1c5b814 last_name: Shen citation: ama: Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024. doi:10.1093/imrn/rnae005 apa: Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae005 chicago: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae005. ieee: S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” International Mathematics Research Notices. Oxford University Press, 2024. ista: Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. mla: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices, Oxford University Press, 2024, doi:10.1093/imrn/rnae005. short: S. Shen, International Mathematics Research Notices (2024). date_created: 2024-02-14T12:16:17Z date_published: 2024-02-05T00:00:00Z date_updated: 2024-02-19T10:22:44Z day: '05' department: - _id: TaHa doi: 10.1093/imrn/rnae005 ec_funded: 1 external_id: arxiv: - '1810.12491' keyword: - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1093/imrn/rnae005 month: '02' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: epub_ahead publisher: Oxford University Press quality_controlled: '1' status: public title: Tamely ramified geometric Langlands correspondence in positive characteristic type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- _id: '12329' abstract: - lang: eng text: In this article, we develop two independent and new approaches to model epidemic spread in a network. Contrary to the most studied models, those developed here allow for contacts with different probabilities of transmitting the disease (transmissibilities). We then examine each of these models using some mean field type approximations. The first model looks at the late-stage effects of an epidemic outbreak and allows for the computation of the probability that a given vertex was infected. This computation is based on a mean field approximation and only depends on the number of contacts and their transmissibilities. This approach shares many similarities with percolation models in networks. The second model we develop is a dynamic model which we analyze using a mean field approximation which highly reduces the dimensionality of the system. In particular, the original system which individually analyses each vertex of the network is reduced to one with as many equations as different transmissibilities. Perhaps the greatest contribution of this article is the observation that, in both these models, the existence and size of an epidemic outbreak are linked to the properties of a matrix which we call the R-matrix. This is a generalization of the basic reproduction number which more precisely characterizes the main routes of infection. acknowledgement: Gonçalo Oliveira is supported by the NOMIS Foundation, Fundação Serrapilheira 1812-27395, by CNPq grants 428959/2018-0 and 307475/2018-2, and by FAPERJ through the grant Jovem Cientista do Nosso Estado E-26/202.793/2019. article_number: '468' article_processing_charge: No article_type: original author: - first_name: Arturo full_name: Gómez, Arturo last_name: Gómez - first_name: Goncalo full_name: Oliveira, Goncalo id: 58abbde8-f455-11eb-a497-98c8fd71b905 last_name: Oliveira citation: ama: Gómez A, Oliveira G. New approaches to epidemic modeling on networks. Scientific Reports. 2023;13. doi:10.1038/s41598-022-19827-9 apa: Gómez, A., & Oliveira, G. (2023). New approaches to epidemic modeling on networks. Scientific Reports. Springer Nature. https://doi.org/10.1038/s41598-022-19827-9 chicago: Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on Networks.” Scientific Reports. Springer Nature, 2023. https://doi.org/10.1038/s41598-022-19827-9. ieee: A. Gómez and G. Oliveira, “New approaches to epidemic modeling on networks,” Scientific Reports, vol. 13. Springer Nature, 2023. ista: Gómez A, Oliveira G. 2023. New approaches to epidemic modeling on networks. Scientific Reports. 13, 468. mla: Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on Networks.” Scientific Reports, vol. 13, 468, Springer Nature, 2023, doi:10.1038/s41598-022-19827-9. short: A. Gómez, G. Oliveira, Scientific Reports 13 (2023). date_created: 2023-01-22T23:00:55Z date_published: 2023-01-10T00:00:00Z date_updated: 2023-08-01T12:31:40Z day: '10' ddc: - '510' department: - _id: TaHa doi: 10.1038/s41598-022-19827-9 external_id: isi: - '001003345000051' file: - access_level: open_access checksum: a8b83739f4a951e83e0b2a778f03b327 content_type: application/pdf creator: dernst date_created: 2023-01-23T07:53:23Z date_updated: 2023-01-23T07:53:23Z file_id: '12336' file_name: 2023_ScientificReports_Gomez.pdf file_size: 2167792 relation: main_file success: 1 file_date_updated: 2023-01-23T07:53:23Z has_accepted_license: '1' intvolume: ' 13' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version publication: Scientific Reports publication_identifier: eissn: - 2045-2322 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: New approaches to epidemic modeling on networks tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 13 year: '2023' ... --- _id: '13966' abstract: - lang: eng text: We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the Møller-Plesset (MPn) perturbation series, obtaining accurate correlation energies up to n=5, with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecular many-fermion correlation problem, opening up the possibility of low-scaling, accurate stochastic computations for a wide class of many-body systems described by Hugenholtz diagrams. acknowledgement: We acknowledge stimulating discussions with Sergey Varganov, Artur Izmaylov, Jacek Kłos, Piotr Żuchowski, Dominika Zgid, Nikolay Prokof'ev, Boris Svistunov, Robert Parrish, and Andreas Heßelmann. G.B. and Q.P.H. acknowledge support from the Austrian Science Fund (FWF) under Projects No. M2641-N27 and No. M2751. M.L. acknowledges support by the FWF under Project No. P29902-N27, and by the European Research Council (ERC) Starting Grant No. 801770 (ANGULON). T.V.T. was supported by the NSF CAREER award No. PHY-2045681. This work is supported by the German Research Foundation (DFG) under Germany's Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster). The authors acknowledge support by the state of Baden-Württemberg through bwHPC. article_number: '045115' article_processing_charge: No article_type: original author: - first_name: Giacomo full_name: Bighin, Giacomo id: 4CA96FD4-F248-11E8-B48F-1D18A9856A87 last_name: Bighin orcid: 0000-0001-8823-9777 - first_name: Quoc P full_name: Ho, Quoc P id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87 last_name: Ho - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 - first_name: T. V. full_name: Tscherbul, T. V. last_name: Tscherbul citation: ama: 'Bighin G, Ho QP, Lemeshko M, Tscherbul TV. Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling. Physical Review B. 2023;108(4). doi:10.1103/PhysRevB.108.045115' apa: 'Bighin, G., Ho, Q. P., Lemeshko, M., & Tscherbul, T. V. (2023). Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling. Physical Review B. American Physical Society. https://doi.org/10.1103/PhysRevB.108.045115' chicago: 'Bighin, Giacomo, Quoc P Ho, Mikhail Lemeshko, and T. V. Tscherbul. “Diagrammatic Monte Carlo for Electronic Correlation in Molecules: High-Order Many-Body Perturbation Theory with Low Scaling.” Physical Review B. American Physical Society, 2023. https://doi.org/10.1103/PhysRevB.108.045115.' ieee: 'G. Bighin, Q. P. Ho, M. Lemeshko, and T. V. Tscherbul, “Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling,” Physical Review B, vol. 108, no. 4. American Physical Society, 2023.' ista: 'Bighin G, Ho QP, Lemeshko M, Tscherbul TV. 2023. Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling. Physical Review B. 108(4), 045115.' mla: 'Bighin, Giacomo, et al. “Diagrammatic Monte Carlo for Electronic Correlation in Molecules: High-Order Many-Body Perturbation Theory with Low Scaling.” Physical Review B, vol. 108, no. 4, 045115, American Physical Society, 2023, doi:10.1103/PhysRevB.108.045115.' short: G. Bighin, Q.P. Ho, M. Lemeshko, T.V. Tscherbul, Physical Review B 108 (2023). date_created: 2023-08-06T22:01:10Z date_published: 2023-07-15T00:00:00Z date_updated: 2023-08-07T08:41:29Z day: '15' department: - _id: MiLe - _id: TaHa doi: 10.1103/PhysRevB.108.045115 ec_funded: 1 external_id: arxiv: - '2203.12666' intvolume: ' 108' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2203.12666 month: '07' oa: 1 oa_version: Preprint project: - _id: 26986C82-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02641 name: A path-integral approach to composite impurities - _id: 26B96266-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02751 name: Algebro-Geometric Applications of Factorization Homology - _id: 26031614-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P29902 name: Quantum rotations in the presence of a many-body environment - _id: 2688CF98-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '801770' name: 'Angulon: physics and applications of a new quasiparticle' publication: Physical Review B publication_identifier: eissn: - 2469-9969 issn: - 2469-9950 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: 'Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 108 year: '2023' ... --- _id: '14239' abstract: - lang: eng text: "Given a resolution of rational singularities π:X~→X over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor \ Rπ∗:Db(X~)→Db(X)\r\n between bounded derived categories of coherent sheaves generates Db(X)\r\n as a triangulated category. This gives a weak version of the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21]. The same result is established more generally for proper (not necessarily birational) morphisms π:X~→X , with X~\r\n smooth, satisfying Rπ∗(OX~)=OX ." acknowledgement: "We thank Agnieszka Bodzenta-Skibińska, Paolo Cascini, Wahei Hara, Sándor Kovács, Alexander Kuznetsov, Mircea Musta ă, Nebojsa Pavic, Pavel Sechin, and Michael Wemyss for discussions and e-mail correspondence. We also thank the anonymous referee for the helpful comments. M.M. was supported by the Institute of Science and Technology Austria. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 101034413. E.S. was partially supported by the EPSRC grant EP/T019379/1 “Derived categories and algebraic K-theory of singularities”, and by the ERC Synergy grant “Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties.”\r\n\r\n" article_number: e66 article_processing_charge: Yes article_type: original author: - first_name: Mirko full_name: Mauri, Mirko id: 2cf70c34-09c1-11ed-bd8d-c34fac206130 last_name: Mauri - first_name: Evgeny full_name: Shinder, Evgeny last_name: Shinder citation: ama: Mauri M, Shinder E. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 2023;11. doi:10.1017/fms.2023.65 apa: Mauri, M., & Shinder, E. (2023). Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.65 chicago: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” Forum of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.65. ieee: M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture for rational singularities,” Forum of Mathematics, Sigma, vol. 11. Cambridge University Press, 2023. ista: Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 11, e66. mla: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” Forum of Mathematics, Sigma, vol. 11, e66, Cambridge University Press, 2023, doi:10.1017/fms.2023.65. short: M. Mauri, E. Shinder, Forum of Mathematics, Sigma 11 (2023). date_created: 2023-08-27T22:01:16Z date_published: 2023-08-03T00:00:00Z date_updated: 2023-12-13T12:18:18Z day: '03' ddc: - '510' department: - _id: TaHa doi: 10.1017/fms.2023.65 ec_funded: 1 external_id: arxiv: - '2212.06786' isi: - '001041926700001' file: - access_level: open_access checksum: c36241750cc5cb06890aec0ecdfee626 content_type: application/pdf creator: dernst date_created: 2023-09-05T06:43:11Z date_updated: 2023-09-05T06:43:11Z file_id: '14266' file_name: 2023_ForumMathematics_Mauri.pdf file_size: 280865 relation: main_file success: 1 file_date_updated: 2023-09-05T06:43:11Z has_accepted_license: '1' intvolume: ' 11' isi: 1 language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Forum of Mathematics, Sigma publication_identifier: eissn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Homological Bondal-Orlov localization conjecture for rational singularities tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2023' ... --- _id: '13268' abstract: - lang: eng text: We give a simple argument to prove Nagai’s conjecture for type II degenerations of compact hyperkähler manifolds and cohomology classes of middle degree. Under an additional assumption, the techniques yield the conjecture in arbitrary degree. This would complete the proof of Nagai’s conjecture in general, as it was proved already for type I degenerations by Kollár, Laza, Saccà, and Voisin [10] and independently by Soldatenkov [18], while it is immediate for type III degenerations. Our arguments are close in spirit to a recent paper by Harder [8] proving similar results for the restrictive class of good degenerations. acknowledgement: The first author is supported by the ERC Synergy Grant HyperK. The second author is supported by the Max Planck Institute for Mathematics and the Institute of Science and Technology Austria. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. article_processing_charge: No article_type: original author: - first_name: D. full_name: Huybrechts, D. last_name: Huybrechts - first_name: Mirko full_name: Mauri, Mirko id: 2cf70c34-09c1-11ed-bd8d-c34fac206130 last_name: Mauri citation: ama: Huybrechts D, Mauri M. On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. 2023;30(1):125-141. doi:10.4310/mrl.2023.v30.n1.a6 apa: Huybrechts, D., & Mauri, M. (2023). On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. International Press. https://doi.org/10.4310/mrl.2023.v30.n1.a6 chicago: Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.” Mathematical Research Letters. International Press, 2023. https://doi.org/10.4310/mrl.2023.v30.n1.a6. ieee: D. Huybrechts and M. Mauri, “On type II degenerations of hyperkähler manifolds,” Mathematical Research Letters, vol. 30, no. 1. International Press, pp. 125–141, 2023. ista: Huybrechts D, Mauri M. 2023. On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. 30(1), 125–141. mla: Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.” Mathematical Research Letters, vol. 30, no. 1, International Press, 2023, pp. 125–41, doi:10.4310/mrl.2023.v30.n1.a6. short: D. Huybrechts, M. Mauri, Mathematical Research Letters 30 (2023) 125–141. date_created: 2023-07-23T22:01:14Z date_published: 2023-06-21T00:00:00Z date_updated: 2024-01-16T12:00:47Z day: '21' department: - _id: TaHa doi: 10.4310/mrl.2023.v30.n1.a6 ec_funded: 1 external_id: arxiv: - '2108.01587' isi: - '001027656000006' intvolume: ' 30' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2108.01587 month: '06' oa: 1 oa_version: Preprint page: 125-141 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Mathematical Research Letters publication_identifier: eissn: - 1945-001X issn: - 1073-2780 publication_status: published publisher: International Press quality_controlled: '1' scopus_import: '1' status: public title: On type II degenerations of hyperkähler manifolds type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2023' ... --- _id: '14244' abstract: - lang: eng text: "In this paper, we determine the motivic class — in particular, the weight polynomial and conjecturally the Poincaré polynomial — of the open de Rham space, defined and studied by Boalch, of certain moduli spaces of irregular meromorphic connections on the trivial rank \r\n bundle on P1. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild character variety. We also identify the open de Rham spaces with quiver varieties with multiplicities of Yamakawa and Geiss–Leclerc–Schröer. We finish with constructing natural complete hyperkähler metrics on them, which in the four-dimensional cases are expected to be of type ALF." acknowledgement: We would like to thank Gergely Bérczy, Roger Bielawski, Philip Boalch, Sergey Cherkis, Andrew Dancer, Brent Doran, Eloïse Hamilton, Frances Kirwan, Bernard Leclerc, Emmanuel Letellier, Alessia Mandini, Maxence Mayrand, András Némethi, Szilárd Szabó, and Daisuke Yamakawa for discussions related to the paper. We especially thank the referee for an extensive list of very careful comments. At various stages of this project, the authors were supported by the Advanced Grant “Arithmetic and physics of Higgs moduli spaces” no. 320593 of the European Research Council, by grant no. 153627 and NCCR SwissMAP, both funded by the Swiss National Science Foundation as well as by EPF Lausanne and IST Austria. In the final stages of this project, MLW was supported by SFB/TR 45 “Periods, moduli and arithmetic of algebraic varieties,” subproject M08-10 “Moduli of vector bundles on higher-dimensional varieties.” DW was also supported by the Fondation Sciences Mathématiques de Paris, as well as public grants overseen by the Agence national de la recherche (ANR) of France as part of the Investissements d'avenir program, under reference numbers ANR-10-LABX-0098 and ANR-15-CE40-0008 (Défigéo). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Michael Lennox full_name: Wong, Michael Lennox last_name: Wong - first_name: Dimitri full_name: Wyss, Dimitri last_name: Wyss citation: ama: Hausel T, Wong ML, Wyss D. Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. 2023;127(4):958-1027. doi:10.1112/plms.12555 apa: Hausel, T., Wong, M. L., & Wyss, D. (2023). Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.12555 chicago: Hausel, Tamás, Michael Lennox Wong, and Dimitri Wyss. “Arithmetic and Metric Aspects of Open de Rham Spaces.” Proceedings of the London Mathematical Society. Wiley, 2023. https://doi.org/10.1112/plms.12555. ieee: T. Hausel, M. L. Wong, and D. Wyss, “Arithmetic and metric aspects of open de Rham spaces,” Proceedings of the London Mathematical Society, vol. 127, no. 4. Wiley, pp. 958–1027, 2023. ista: Hausel T, Wong ML, Wyss D. 2023. Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. 127(4), 958–1027. mla: Hausel, Tamás, et al. “Arithmetic and Metric Aspects of Open de Rham Spaces.” Proceedings of the London Mathematical Society, vol. 127, no. 4, Wiley, 2023, pp. 958–1027, doi:10.1112/plms.12555. short: T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society 127 (2023) 958–1027. date_created: 2023-08-27T22:01:18Z date_published: 2023-10-01T00:00:00Z date_updated: 2024-01-30T12:56:10Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1112/plms.12555 ec_funded: 1 external_id: arxiv: - '1807.04057' isi: - '001049312700001' file: - access_level: open_access checksum: 2af4d2d6a8ae42f7d3fba0188e79ae82 content_type: application/pdf creator: dernst date_created: 2024-01-30T12:56:00Z date_updated: 2024-01-30T12:56:00Z file_id: '14910' file_name: 2023_ProcLondonMathSoc_Hausel.pdf file_size: 651335 relation: main_file success: 1 file_date_updated: 2024-01-30T12:56:00Z has_accepted_license: '1' intvolume: ' 127' isi: 1 issue: '4' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 958-1027 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces - _id: 25E6C798-B435-11E9-9278-68D0E5697425 grant_number: '153627' name: Arithmetic quantization of character and quiver varities publication: Proceedings of the London Mathematical Society publication_identifier: eissn: - 1460-244X issn: - 0024-6115 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Arithmetic and metric aspects of open de Rham spaces tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 127 year: '2023' ... --- _id: '12303' abstract: - lang: eng text: We construct for each choice of a quiver Q, a cohomology theory A, and a poset P a “loop Grassmannian” GP(Q,A). This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms. The addition of a “dilation” torus D⊆G2m gives a quantization GPD(Q,A). This construction is motivated by the program of introducing an inner cohomology theory in algebraic geometry adequate for the Geometric Langlands program (Mirković, Some extensions of the notion of loop Grassmannians. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardešić issue. No. 532, 53–74, 2017) and on the construction of affine quantum groups from generalized cohomology theories (Yang and Zhao, Quiver varieties and elliptic quantum groups, preprint. arxiv1708.01418). acknowledgement: I.M. thanks Zhijie Dong for long-term discussions on the material that entered this work. We thank Misha Finkelberg for pointing out errors in earlier versions. His advice and his insistence have led to a much better paper. A part of the writing was done at the conference at IST (Vienna) attended by all coauthors. We therefore thank the organizers of the conference and the support of ERC Advanced Grant Arithmetic and Physics of Higgs moduli spaces No. 320593. The work of I.M. was partially supported by NSF grants. The work of Y.Y. was partially supported by the Australian Research Council (ARC) via the award DE190101231. The work of G.Z. was partially supported by ARC via the award DE190101222. alternative_title: - Trends in Mathematics article_processing_charge: No author: - first_name: Ivan full_name: Mirković, Ivan last_name: Mirković - first_name: Yaping full_name: Yang, Yaping last_name: Yang - first_name: Gufang full_name: Zhao, Gufang id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87 last_name: Zhao citation: ama: 'Mirković I, Yang Y, Zhao G. Loop Grassmannians of Quivers and Affine Quantum Groups. In: Baranovskky V, Guay N, Schedler T, eds. Representation Theory and Algebraic Geometry. 1st ed. TM. Cham: Springer Nature; Birkhäuser; 2022:347-392. doi:10.1007/978-3-030-82007-7_8' apa: 'Mirković, I., Yang, Y., & Zhao, G. (2022). Loop Grassmannians of Quivers and Affine Quantum Groups. In V. Baranovskky, N. Guay, & T. Schedler (Eds.), Representation Theory and Algebraic Geometry (1st ed., pp. 347–392). Cham: Springer Nature; Birkhäuser. https://doi.org/10.1007/978-3-030-82007-7_8' chicago: 'Mirković, Ivan, Yaping Yang, and Gufang Zhao. “Loop Grassmannians of Quivers and Affine Quantum Groups.” In Representation Theory and Algebraic Geometry, edited by Vladimir Baranovskky, Nicolas Guay, and Travis Schedler, 1st ed., 347–92. TM. Cham: Springer Nature; Birkhäuser, 2022. https://doi.org/10.1007/978-3-030-82007-7_8.' ieee: 'I. Mirković, Y. Yang, and G. Zhao, “Loop Grassmannians of Quivers and Affine Quantum Groups,” in Representation Theory and Algebraic Geometry, 1st ed., V. Baranovskky, N. Guay, and T. Schedler, Eds. Cham: Springer Nature; Birkhäuser, 2022, pp. 347–392.' ista: 'Mirković I, Yang Y, Zhao G. 2022.Loop Grassmannians of Quivers and Affine Quantum Groups. In: Representation Theory and Algebraic Geometry. Trends in Mathematics, , 347–392.' mla: Mirković, Ivan, et al. “Loop Grassmannians of Quivers and Affine Quantum Groups.” Representation Theory and Algebraic Geometry, edited by Vladimir Baranovskky et al., 1st ed., Springer Nature; Birkhäuser, 2022, pp. 347–92, doi:10.1007/978-3-030-82007-7_8. short: I. Mirković, Y. Yang, G. Zhao, in:, V. Baranovskky, N. Guay, T. Schedler (Eds.), Representation Theory and Algebraic Geometry, 1st ed., Springer Nature; Birkhäuser, Cham, 2022, pp. 347–392. date_created: 2023-01-16T10:06:41Z date_published: 2022-06-16T00:00:00Z date_updated: 2023-01-27T07:07:31Z day: '16' department: - _id: TaHa doi: 10.1007/978-3-030-82007-7_8 ec_funded: 1 edition: '1' editor: - first_name: Vladimir full_name: Baranovskky, Vladimir last_name: Baranovskky - first_name: Nicolas full_name: Guay, Nicolas last_name: Guay - first_name: Travis full_name: Schedler, Travis last_name: Schedler external_id: arxiv: - '1810.10095' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1810.10095 month: '06' oa: 1 oa_version: Preprint page: 347-392 place: Cham project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Representation Theory and Algebraic Geometry publication_identifier: eisbn: - '9783030820077' eissn: - 2297-024X isbn: - '9783030820060' issn: - 2297-0215 publication_status: published publisher: Springer Nature; Birkhäuser quality_controlled: '1' scopus_import: '1' series_title: TM status: public title: Loop Grassmannians of Quivers and Affine Quantum Groups type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2022' ... --- _id: '9977' abstract: - lang: eng text: "For a Seifert fibered homology sphere X we show that the q-series invariant Zˆ0(X; q) introduced by Gukov-Pei-Putrov-Vafa, is a resummation of the Ohtsuki series Z0(X). We show that for every even k ∈ N there exists a full asymptotic expansion of Zˆ0(X; q) for q tending to e 2πi/k, and in particular that the limit Zˆ0(X; e 2πi/k) exists and is equal to the\r\nWRT quantum invariant τk(X). We show that the poles of the Borel transform of Z0(X) coincide with the classical complex Chern-Simons values, which we further show classifies the corresponding components of the moduli space of flat SL(2, C)-connections." acknowledgement: "We warmly thank S. Gukov for valuable discussions on the GPPV invariant ̂Z\U0001D44E(\U0001D4403; \U0001D45E). The first\r\nauthor was supported in part by the center of excellence grant ‘Center for Quantum Geometry\r\nof Moduli Spaces’ from the Danish National Research Foundation (DNRF95) and by the ERCSynergy\r\ngrant ‘ReNewQuantum’. The second author received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 754411." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: William full_name: Mistegaard, William id: 41B03CD0-62AE-11E9-84EF-0718E6697425 last_name: Mistegaard - first_name: Jørgen Ellegaard full_name: Andersen, Jørgen Ellegaard last_name: Andersen citation: ama: Mistegaard W, Andersen JE. Resurgence analysis of quantum invariants of Seifert fibered homology spheres. Journal of the London Mathematical Society. 2022;105(2):709-764. doi:10.1112/jlms.12506 apa: Mistegaard, W., & Andersen, J. E. (2022). Resurgence analysis of quantum invariants of Seifert fibered homology spheres. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12506 chicago: Mistegaard, William, and Jørgen Ellegaard Andersen. “Resurgence Analysis of Quantum Invariants of Seifert Fibered Homology Spheres.” Journal of the London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12506. ieee: W. Mistegaard and J. E. Andersen, “Resurgence analysis of quantum invariants of Seifert fibered homology spheres,” Journal of the London Mathematical Society, vol. 105, no. 2. Wiley, pp. 709–764, 2022. ista: Mistegaard W, Andersen JE. 2022. Resurgence analysis of quantum invariants of Seifert fibered homology spheres. Journal of the London Mathematical Society. 105(2), 709–764. mla: Mistegaard, William, and Jørgen Ellegaard Andersen. “Resurgence Analysis of Quantum Invariants of Seifert Fibered Homology Spheres.” Journal of the London Mathematical Society, vol. 105, no. 2, Wiley, 2022, pp. 709–64, doi:10.1112/jlms.12506. short: W. Mistegaard, J.E. Andersen, Journal of the London Mathematical Society 105 (2022) 709–764. date_created: 2021-08-31T12:51:40Z date_published: 2022-03-01T00:00:00Z date_updated: 2023-08-02T06:53:51Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1112/jlms.12506 ec_funded: 1 external_id: arxiv: - '1811.05376' isi: - '000755205700001' file: - access_level: open_access checksum: 9c72327d39f34f1a6eaa98fa4b8493f2 content_type: application/pdf creator: dernst date_created: 2022-03-24T11:42:25Z date_updated: 2022-03-24T11:42:25Z file_id: '10917' file_name: 2022_JourLondonMathSoc_Andersen.pdf file_size: 649130 relation: main_file success: 1 file_date_updated: 2022-03-24T11:42:25Z has_accepted_license: '1' intvolume: ' 105' isi: 1 issue: '2' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 709-764 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Resurgence analysis of quantum invariants of Seifert fibered homology spheres tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 105 year: '2022' ... --- _id: '10704' abstract: - lang: eng text: We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ingredients are the Bialynicki-Birula theory of C∗-actions on semiprojective varieties, C∗ characters of indices of C∗-equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier–Mukai transform along the Hitchin fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs bundles. acknowledgement: We would like to thank Brian Collier, Davide Gaiotto, Peter Gothen, Jochen Heinloth, Daniel Huybrechts, Quoc Ho, Joel Kamnitzer, Gérard Laumon, Luca Migliorini, Alexander Minets, Brent Pym, Peng Shan, Carlos Simpson, András Szenes, Fernando R. Villegas, Richard Wentworth, Edward Witten and Kōta Yoshioka for interesting comments and discussions. Most of all we are grateful for a long list of very helpful comments by the referee. We would also like to thank the organizers of the Summer School on Higgs bundles in Hamburg in September 2018, where the authors and Richard Wentworth were giving lectures and where the work in this paper started by considering the mirror of the Lagrangian upward flows W+E investigated in [17]. The second author wishes to thank EPSRC and ICMAT for support. Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Nigel full_name: Hitchin, Nigel last_name: Hitchin citation: ama: Hausel T, Hitchin N. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. 2022;228:893-989. doi:10.1007/s00222-021-01093-7 apa: Hausel, T., & Hitchin, N. (2022). Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-021-01093-7 chicago: Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” Inventiones Mathematicae. Springer Nature, 2022. https://doi.org/10.1007/s00222-021-01093-7. ieee: T. Hausel and N. Hitchin, “Very stable Higgs bundles, equivariant multiplicity and mirror symmetry,” Inventiones Mathematicae, vol. 228. Springer Nature, pp. 893–989, 2022. ista: Hausel T, Hitchin N. 2022. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. 228, 893–989. mla: Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” Inventiones Mathematicae, vol. 228, Springer Nature, 2022, pp. 893–989, doi:10.1007/s00222-021-01093-7. short: T. Hausel, N. Hitchin, Inventiones Mathematicae 228 (2022) 893–989. date_created: 2022-01-30T23:01:34Z date_published: 2022-05-01T00:00:00Z date_updated: 2023-08-02T14:03:20Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1007/s00222-021-01093-7 external_id: arxiv: - '2101.08583' isi: - '000745495400001' file: - access_level: open_access checksum: a382ba75acebc9adfb8fe56247cb410e content_type: application/pdf creator: dernst date_created: 2023-02-27T07:30:47Z date_updated: 2023-02-27T07:30:47Z file_id: '12687' file_name: 2022_InventionesMahtematicae_Hausel.pdf file_size: 1069538 relation: main_file success: 1 file_date_updated: 2023-02-27T07:30:47Z has_accepted_license: '1' intvolume: ' 228' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 893-989 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Inventiones Mathematicae publication_identifier: eissn: - 1432-1297 issn: - 0020-9910 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - description: News on the ISTA Website relation: press_release url: https://ista.ac.at/en/news/the-tip-of-the-mathematical-iceberg/ scopus_import: '1' status: public title: Very stable Higgs bundles, equivariant multiplicity and mirror symmetry tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 228 year: '2022' ... --- _id: '10772' abstract: - lang: eng text: We introduce tropical corals, balanced trees in a half-space, and show that they correspond to holomorphic polygons capturing the product rule in Lagrangian Floer theory for the elliptic curve. We then prove a correspondence theorem equating counts of tropical corals to punctured log Gromov–Witten invariants of the Tate curve. This implies that the homogeneous coordinate ring of the mirror to the Tate curve is isomorphic to the degree-zero part of symplectic cohomology, confirming a prediction of homological mirror symmetry. acknowledgement: 'This paper is based on my PhD thesis, which would not be possible without the support of my advisor Bernd Siebert. I also thank Dan Abramovich, Mohammed Abouzaid, Mark Gross, Tom Coates and Dimitri Zvonkine for many useful conversations. Finally, I thank the anonymous referees for their many insightful comments and valuable suggestions which have resulted in major improvements to this article. This project has received funding from the EuropeanResearch Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement Number: 682603), and from Fondation Mathématique Jacques Hadamard. ' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Nuroemuer Huelya full_name: Arguez, Nuroemuer Huelya id: 3c26b22e-c843-11eb-aa56-d38ffa0bdd08 last_name: Arguez citation: ama: Arguez NH. Mirror symmetry for the Tate curve via tropical and log corals. Journal of the London Mathematical Society. 2022;105(1):343-411. doi:10.1112/jlms.12515 apa: Arguez, N. H. (2022). Mirror symmetry for the Tate curve via tropical and log corals. Journal of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/jlms.12515 chicago: Arguez, Nuroemuer Huelya. “Mirror Symmetry for the Tate Curve via Tropical and Log Corals.” Journal of the London Mathematical Society. London Mathematical Society, 2022. https://doi.org/10.1112/jlms.12515. ieee: N. H. Arguez, “Mirror symmetry for the Tate curve via tropical and log corals,” Journal of the London Mathematical Society, vol. 105, no. 1. London Mathematical Society, pp. 343–411, 2022. ista: Arguez NH. 2022. Mirror symmetry for the Tate curve via tropical and log corals. Journal of the London Mathematical Society. 105(1), 343–411. mla: Arguez, Nuroemuer Huelya. “Mirror Symmetry for the Tate Curve via Tropical and Log Corals.” Journal of the London Mathematical Society, vol. 105, no. 1, London Mathematical Society, 2022, pp. 343–411, doi:10.1112/jlms.12515. short: N.H. Arguez, Journal of the London Mathematical Society 105 (2022) 343–411. date_created: 2022-02-20T23:01:33Z date_published: 2022-02-05T00:00:00Z date_updated: 2023-08-02T14:29:50Z day: '05' ddc: - '510' department: - _id: TaHa doi: 10.1112/jlms.12515 external_id: arxiv: - '1712.10260' isi: - '000751600600001' file: - access_level: open_access checksum: 8bd0fd9694be894a191857ddf27678f0 content_type: application/pdf creator: dernst date_created: 2022-02-21T11:22:58Z date_updated: 2022-02-21T11:22:58Z file_id: '10783' file_name: 2022_JournLondonMathSociety_Arguez.pdf file_size: 936873 relation: main_file success: 1 file_date_updated: 2022-02-21T11:22:58Z has_accepted_license: '1' intvolume: ' 105' isi: 1 issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '02' oa: 1 oa_version: Published Version page: 343-411 publication: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 issn: - 0024-6107 publication_status: published publisher: London Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Mirror symmetry for the Tate curve via tropical and log corals tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 105 year: '2022' ... --- _id: '12793' abstract: - lang: eng text: "Let F be a global function field with constant field Fq. Let G be a reductive group over Fq. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original construction. We establish a coarse geometric expansion for our variant truncation.\r\nAs applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line P1Fq with two points of ramifications." acknowledgement: 'I’d like to thank Prof. Chaudouard for introducing me to this area. I’d like to thank Prof. Harris for asking me the question that makes Section 10 possible. I’m grateful for the support of Prof. Hausel and IST Austria. The author was funded by an ISTplus fellowship: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.' article_processing_charge: No article_type: original author: - first_name: Hongjie full_name: Yu, Hongjie id: 3D7DD9BE-F248-11E8-B48F-1D18A9856A87 last_name: Yu orcid: 0000-0001-5128-7126 citation: ama: Yu H. A coarse geometric expansion of a variant of Arthur’s truncated traces and some applications. Pacific Journal of Mathematics. 2022;321(1):193-237. doi:10.2140/pjm.2022.321.193 apa: Yu, H. (2022). A coarse geometric expansion of a variant of Arthur’s truncated traces and some applications. Pacific Journal of Mathematics. Mathematical Sciences Publishers. https://doi.org/10.2140/pjm.2022.321.193 chicago: Yu, Hongjie. “ A Coarse Geometric Expansion of a Variant of Arthur’s Truncated Traces and Some Applications.” Pacific Journal of Mathematics. Mathematical Sciences Publishers, 2022. https://doi.org/10.2140/pjm.2022.321.193. ieee: H. Yu, “ A coarse geometric expansion of a variant of Arthur’s truncated traces and some applications,” Pacific Journal of Mathematics, vol. 321, no. 1. Mathematical Sciences Publishers, pp. 193–237, 2022. ista: Yu H. 2022. A coarse geometric expansion of a variant of Arthur’s truncated traces and some applications. Pacific Journal of Mathematics. 321(1), 193–237. mla: Yu, Hongjie. “ A Coarse Geometric Expansion of a Variant of Arthur’s Truncated Traces and Some Applications.” Pacific Journal of Mathematics, vol. 321, no. 1, Mathematical Sciences Publishers, 2022, pp. 193–237, doi:10.2140/pjm.2022.321.193. short: H. Yu, Pacific Journal of Mathematics 321 (2022) 193–237. date_created: 2023-04-02T22:01:11Z date_published: 2022-08-29T00:00:00Z date_updated: 2023-08-04T10:42:38Z day: '29' department: - _id: TaHa doi: 10.2140/pjm.2022.321.193 ec_funded: 1 external_id: arxiv: - '2109.10245' isi: - '000954466300006' intvolume: ' 321' isi: 1 issue: '1' keyword: - Arthur–Selberg trace formula - cuspidal automorphic representations - global function fields language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2109.10245 month: '08' oa: 1 oa_version: Preprint page: 193-237 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Pacific Journal of Mathematics publication_identifier: eissn: - 1945-5844 issn: - 0030-8730 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: ' A coarse geometric expansion of a variant of Arthur''s truncated traces and some applications' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 321 year: '2022' ... --- _id: '6965' abstract: - lang: eng text: The central object of investigation of this paper is the Hirzebruch class, a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following the work of Weber, we investigate its equivariant version for (possibly singular) toric varieties. The local decomposition of the Hirzebruch class to the fixed points of the torus action and a formula for the local class in terms of the defining fan are recalled. After this review part, we prove the positivity of local Hirzebruch classes for all toric varieties, thus proving false the alleged counterexample given by Weber. article_processing_charge: No article_type: original author: - first_name: Kamil P full_name: Rychlewicz, Kamil P id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425 last_name: Rychlewicz citation: ama: Rychlewicz KP. The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society. 2021;53(2):560-574. doi:10.1112/blms.12442 apa: Rychlewicz, K. P. (2021). The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society. Wiley. https://doi.org/10.1112/blms.12442 chicago: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” Bulletin of the London Mathematical Society. Wiley, 2021. https://doi.org/10.1112/blms.12442. ieee: K. P. Rychlewicz, “The positivity of local equivariant Hirzebruch class for toric varieties,” Bulletin of the London Mathematical Society, vol. 53, no. 2. Wiley, pp. 560–574, 2021. ista: Rychlewicz KP. 2021. The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society. 53(2), 560–574. mla: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” Bulletin of the London Mathematical Society, vol. 53, no. 2, Wiley, 2021, pp. 560–74, doi:10.1112/blms.12442. short: K.P. Rychlewicz, Bulletin of the London Mathematical Society 53 (2021) 560–574. date_created: 2019-10-24T08:04:09Z date_published: 2021-04-01T00:00:00Z date_updated: 2023-08-04T10:43:39Z day: '01' department: - _id: TaHa doi: 10.1112/blms.12442 external_id: arxiv: - '1910.10435' isi: - '000594805800001' intvolume: ' 53' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.10435 month: '04' oa: 1 oa_version: Preprint page: 560-574 publication: Bulletin of the London Mathematical Society publication_identifier: eissn: - 1469-2120 issn: - 0024-6093 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: The positivity of local equivariant Hirzebruch class for toric varieties type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 53 year: '2021' ... --- _id: '9099' abstract: - lang: eng text: We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to a field of characteristic zero as a morphism vanishes if and only if it vanishes for lifting it as a derived autoequivalence. We also compare the deformation space of these two types of deformations. acknowledgement: I would like to thank Piotr Achinger, Daniel Huybrechts, Katrina Honigs, Marcin Lara, and Maciek Zdanowicz for the mathematical discussions, Tamas Hausel for hosting me in his research group at IST Austria, and the referees for their valuable suggestions. This research has received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie Grant Agreement No. 754411. article_processing_charge: No article_type: original author: - first_name: Tanya K full_name: Srivastava, Tanya K id: 4D046628-F248-11E8-B48F-1D18A9856A87 last_name: Srivastava citation: ama: Srivastava TK. Lifting automorphisms on Abelian varieties as derived autoequivalences. Archiv der Mathematik. 2021;116(5):515-527. doi:10.1007/s00013-020-01564-y apa: Srivastava, T. K. (2021). Lifting automorphisms on Abelian varieties as derived autoequivalences. Archiv Der Mathematik. Springer Nature. https://doi.org/10.1007/s00013-020-01564-y chicago: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences.” Archiv Der Mathematik. Springer Nature, 2021. https://doi.org/10.1007/s00013-020-01564-y. ieee: T. K. Srivastava, “Lifting automorphisms on Abelian varieties as derived autoequivalences,” Archiv der Mathematik, vol. 116, no. 5. Springer Nature, pp. 515–527, 2021. ista: Srivastava TK. 2021. Lifting automorphisms on Abelian varieties as derived autoequivalences. Archiv der Mathematik. 116(5), 515–527. mla: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences.” Archiv Der Mathematik, vol. 116, no. 5, Springer Nature, 2021, pp. 515–27, doi:10.1007/s00013-020-01564-y. short: T.K. Srivastava, Archiv Der Mathematik 116 (2021) 515–527. date_created: 2021-02-07T23:01:13Z date_published: 2021-05-01T00:00:00Z date_updated: 2023-08-07T13:42:38Z day: '01' department: - _id: TaHa doi: 10.1007/s00013-020-01564-y ec_funded: 1 external_id: arxiv: - '2001.07762' isi: - '000612580200001' intvolume: ' 116' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2001.07762 month: '05' oa: 1 oa_version: Preprint page: 515-527 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Archiv der Mathematik publication_identifier: eissn: - '14208938' issn: - 0003889X publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Lifting automorphisms on Abelian varieties as derived autoequivalences type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 116 year: '2021' ... --- _id: '9173' abstract: - lang: eng text: We show that Hilbert schemes of points on supersingular Enriques surface in characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties but are not irreducible symplectic as the hodge number h2,0 > 1, even though a supersingular Enriques surface is an irreducible symplectic variety. These are the classes of varieties which appear only in characteristic 2 and they show that the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor Calabi-Yau, thereby showing that there are strictly more classes of simply connected varieties with trivial canonical class in characteristic 2 than over C as given by Beauville-Bogolomov decomposition theorem. acknowledgement: I would like to thank M. Zdanwociz for various mathematical discussions which lead to this article, Tamas Hausel for hosting me in his research group at IST Austria and the anonymous referee for their helpful suggestions and comments. This research has received funding from the European Union's Horizon 2020 Marie Sklodowska-Curie Actions Grant No. 754411 and Institue of Science and Technology Austria IST-PLUS Grant No. 754411. article_number: '102957' article_processing_charge: No article_type: original author: - first_name: Tanya K full_name: Srivastava, Tanya K id: 4D046628-F248-11E8-B48F-1D18A9856A87 last_name: Srivastava citation: ama: Srivastava TK. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin des Sciences Mathematiques. 2021;167(03). doi:10.1016/j.bulsci.2021.102957 apa: Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin Des Sciences Mathematiques. Elsevier. https://doi.org/10.1016/j.bulsci.2021.102957 chicago: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” Bulletin Des Sciences Mathematiques. Elsevier, 2021. https://doi.org/10.1016/j.bulsci.2021.102957. ieee: T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular Enriques surface,” Bulletin des Sciences Mathematiques, vol. 167, no. 03. Elsevier, 2021. ista: Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957. mla: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” Bulletin Des Sciences Mathematiques, vol. 167, no. 03, 102957, Elsevier, 2021, doi:10.1016/j.bulsci.2021.102957. short: T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021). date_created: 2021-02-21T23:01:20Z date_published: 2021-03-01T00:00:00Z date_updated: 2023-08-07T13:47:48Z day: '01' department: - _id: TaHa doi: 10.1016/j.bulsci.2021.102957 ec_funded: 1 external_id: arxiv: - '2010.08976' isi: - '000623881600009' intvolume: ' 167' isi: 1 issue: '03' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2010.08976 month: '03' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Bulletin des Sciences Mathematiques publication_identifier: issn: - 0007-4497 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Pathologies of the Hilbert scheme of points of a supersingular Enriques surface type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 167 year: '2021' ... --- _id: '9359' abstract: - lang: eng text: "We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras, we obtain new expressions for the cohomologies of the latter. As a consequence, we obtain a uniform and conceptual approach for treating homological stability, homological densities, and arithmetic densities of generalized configuration spaces. Our results categorify, generalize, and in fact provide a conceptual understanding of the coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of the stable homological densities also yields rational homotopy types, answering a question posed by Vakil--Wood. Our approach hinges on the study of homological stability of cohomological Chevalley complexes, which is of independent interest.\r\n" acknowledgement: "This paper owes an obvious intellectual debt to the illuminating treatments of factorization homology by J.\r\nFrancis, D. Gaitsgory, and J. Lurie in [GL,G1, FG]. The author would like to thank B. Farb and J. Wolfson for\r\nbringing the question of explaining coincidences in homological densities to his attention. Moreover, the author\r\nthanks J. Wolfson for many helpful conversations on the subject, O. Randal-Williams for many comments which\r\ngreatly help improve the exposition, and G. C. Drummond-Cole for many useful conversations on L∞-algebras.\r\nFinally, the author is grateful to the anonymous referee for carefully reading the manuscript and for providing\r\nnumerous comments which greatly helped improve the clarity and precision of the exposition.\r\nThis work is supported by the Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 of\r\nthe European Research Council and the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization\r\nHomology,” Austrian Science Fund (FWF): M 2751." article_processing_charge: No article_type: original author: - first_name: Quoc P full_name: Ho, Quoc P id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87 last_name: Ho citation: ama: Ho QP. Homological stability and densities of generalized configuration spaces. Geometry & Topology. 2021;25(2):813-912. doi:10.2140/gt.2021.25.813 apa: Ho, Q. P. (2021). Homological stability and densities of generalized configuration spaces. Geometry & Topology. Mathematical Sciences Publishers. https://doi.org/10.2140/gt.2021.25.813 chicago: Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” Geometry & Topology. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/gt.2021.25.813. ieee: Q. P. Ho, “Homological stability and densities of generalized configuration spaces,” Geometry & Topology, vol. 25, no. 2. Mathematical Sciences Publishers, pp. 813–912, 2021. ista: Ho QP. 2021. Homological stability and densities of generalized configuration spaces. Geometry & Topology. 25(2), 813–912. mla: Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” Geometry & Topology, vol. 25, no. 2, Mathematical Sciences Publishers, 2021, pp. 813–912, doi:10.2140/gt.2021.25.813. short: Q.P. Ho, Geometry & Topology 25 (2021) 813–912. date_created: 2021-05-02T06:59:33Z date_published: 2021-04-27T00:00:00Z date_updated: 2023-08-08T13:28:59Z day: '27' ddc: - '514' - '516' - '512' department: - _id: TaHa doi: 10.2140/gt.2021.25.813 ec_funded: 1 external_id: arxiv: - '1802.07948' isi: - '000682738600005' file: - access_level: open_access checksum: 643a8d2d6f06f0888dcd7503f55d0920 content_type: application/pdf creator: qho date_created: 2021-05-03T06:54:06Z date_updated: 2021-05-03T06:54:06Z file_id: '9366' file_name: densities.pdf file_size: 479268 relation: main_file success: 1 file_date_updated: 2021-05-03T06:54:06Z has_accepted_license: '1' intvolume: ' 25' isi: 1 issue: '2' keyword: - Generalized configuration spaces - homological stability - homological densities - chiral algebras - chiral homology - factorization algebras - Koszul duality - Ran space language: - iso: eng month: '04' oa: 1 oa_version: Submitted Version page: 813-912 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces - _id: 26B96266-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02751 name: Algebro-Geometric Applications of Factorization Homology publication: Geometry & Topology publication_identifier: issn: - 1364-0380 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' status: public title: Homological stability and densities of generalized configuration spaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 25 year: '2021' ... --- _id: '9998' abstract: - lang: eng text: We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice. acknowledgement: 'First of all we would like to thank Andrei Okounkov for invaluable discussions, advises and sharing with us his fantastic viewpoint on modern quantum geometry. We are also grateful to D. Korb and Z. Zhou for their interest and comments. The work of A. Smirnov was supported in part by RFBR Grants under Numbers 15-02-04175 and 15-01-04217 and in part by NSF Grant DMS–2054527. The work of P. Koroteev, A.M. Zeitlin and A. Smirnov is supported in part by AMS Simons travel Grant. A. M. Zeitlin is partially supported by Simons Collaboration Grant, Award ID: 578501. Open access funding provided by Institute of Science and Technology (IST Austria).' article_number: '87' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Peter full_name: Koroteev, Peter last_name: Koroteev - first_name: Petr full_name: Pushkar, Petr id: 151DCEB6-9EC3-11E9-8480-ABECE5697425 last_name: Pushkar - first_name: Andrey V. full_name: Smirnov, Andrey V. last_name: Smirnov - first_name: Anton M. full_name: Zeitlin, Anton M. last_name: Zeitlin citation: ama: Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 2021;27(5). doi:10.1007/s00029-021-00698-3 apa: Koroteev, P., Pushkar, P., Smirnov, A. V., & Zeitlin, A. M. (2021). Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. Springer Nature. https://doi.org/10.1007/s00029-021-00698-3 chicago: Koroteev, Peter, Petr Pushkar, Andrey V. Smirnov, and Anton M. Zeitlin. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” Selecta Mathematica. Springer Nature, 2021. https://doi.org/10.1007/s00029-021-00698-3. ieee: P. Koroteev, P. Pushkar, A. V. Smirnov, and A. M. Zeitlin, “Quantum K-theory of quiver varieties and many-body systems,” Selecta Mathematica, vol. 27, no. 5. Springer Nature, 2021. ista: Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. 2021. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 27(5), 87. mla: Koroteev, Peter, et al. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” Selecta Mathematica, vol. 27, no. 5, 87, Springer Nature, 2021, doi:10.1007/s00029-021-00698-3. short: P. Koroteev, P. Pushkar, A.V. Smirnov, A.M. Zeitlin, Selecta Mathematica 27 (2021). date_created: 2021-09-12T22:01:22Z date_published: 2021-08-30T00:00:00Z date_updated: 2023-08-14T06:34:14Z day: '30' ddc: - '530' department: - _id: TaHa doi: 10.1007/s00029-021-00698-3 external_id: isi: - '000692795200001' file: - access_level: open_access checksum: beadc5a722ffb48190e1e63ee2dbfee5 content_type: application/pdf creator: cchlebak date_created: 2021-09-13T11:31:34Z date_updated: 2021-09-13T11:31:34Z file_id: '10010' file_name: 2021_SelectaMath_Koroteev.pdf file_size: 584648 relation: main_file success: 1 file_date_updated: 2021-09-13T11:31:34Z has_accepted_license: '1' intvolume: ' 27' isi: 1 issue: '5' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Selecta Mathematica publication_identifier: eissn: - 1420-9020 issn: - 1022-1824 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Quantum K-theory of quiver varieties and many-body systems tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 27 year: '2021' ... --- _id: '10033' abstract: - lang: eng text: The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5]. acknowledgement: 'The author would like to express his gratitude to D. Gaitsgory, without whose tireless guidance and encouragement in pursuing this problem, this work would not have been possible. The author is grateful to his advisor B.C. Ngô for many years of patient guidance and support. This paper is revised while the author is a postdoc in Hausel group at IST Austria. We thank him and the group for providing a wonderful research environment. The author also gratefully acknowledges the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization Homology,” Austrian Science Fund (FWF): M 2751.' article_number: '107992' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Quoc P full_name: Ho, Quoc P id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87 last_name: Ho orcid: 0000-0001-6889-1418 citation: ama: Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 2021;392. doi:10.1016/j.aim.2021.107992 apa: Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107992 chicago: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107992. ieee: Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” Advances in Mathematics, vol. 392. Elsevier, 2021. ista: Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992. mla: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” Advances in Mathematics, vol. 392, 107992, Elsevier, 2021, doi:10.1016/j.aim.2021.107992. short: Q.P. Ho, Advances in Mathematics 392 (2021). date_created: 2021-09-21T15:58:59Z date_published: 2021-09-21T00:00:00Z date_updated: 2023-08-14T06:54:35Z day: '21' ddc: - '514' department: - _id: TaHa doi: 10.1016/j.aim.2021.107992 external_id: arxiv: - '1610.00212' isi: - '000707040300031' file: - access_level: open_access checksum: f3c0086d41af11db31c00014efb38072 content_type: application/pdf creator: qho date_created: 2021-09-21T15:58:52Z date_updated: 2021-09-21T15:58:52Z file_id: '10034' file_name: 1-s2.0-S000187082100431X-main.pdf file_size: 840635 relation: main_file file_date_updated: 2021-09-21T15:58:52Z has_accepted_license: '1' intvolume: ' 392' isi: 1 keyword: - Chiral algebras - Chiral homology - Factorization algebras - Koszul duality - Ran space language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 26B96266-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02751 name: Algebro-Geometric Applications of Factorization Homology publication: Advances in Mathematics publication_identifier: eissn: - 1090-2082 issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: The Atiyah-Bott formula and connectivity in chiral Koszul duality tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 392 year: '2021' ... --- _id: '7004' abstract: - lang: eng text: We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds. article_processing_charge: No article_type: original author: - first_name: Miroslav full_name: Rapcak, Miroslav last_name: Rapcak - first_name: Yan full_name: Soibelman, Yan last_name: Soibelman - first_name: Yaping full_name: Yang, Yaping last_name: Yang - first_name: Gufang full_name: Zhao, Gufang id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87 last_name: Zhao citation: ama: Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 2020;376:1803-1873. doi:10.1007/s00220-019-03575-5 apa: Rapcak, M., Soibelman, Y., Yang, Y., & Zhao, G. (2020). Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03575-5 chicago: Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03575-5. ieee: M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras, vertex algebras and instantons,” Communications in Mathematical Physics, vol. 376. Springer Nature, pp. 1803–1873, 2020. ista: Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873. mla: Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical Physics, vol. 376, Springer Nature, 2020, pp. 1803–73, doi:10.1007/s00220-019-03575-5. short: M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical Physics 376 (2020) 1803–1873. date_created: 2019-11-12T14:01:27Z date_published: 2020-06-01T00:00:00Z date_updated: 2023-08-17T14:02:59Z day: '01' department: - _id: TaHa doi: 10.1007/s00220-019-03575-5 ec_funded: 1 external_id: arxiv: - '1810.10402' isi: - '000536255500004' intvolume: ' 376' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1810.10402 month: '06' oa: 1 oa_version: Preprint page: 1803-1873 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Cohomological Hall algebras, vertex algebras and instantons type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 376 year: '2020' ... --- _id: '7683' abstract: - lang: eng text: For any free oriented Borel–Moore homology theory A, we construct an associative product on the A-theory of the stack of Higgs torsion sheaves over a projective curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel–Moore homology groups. We also introduce moduli spaces of stable triples, heavily inspired by Nakajima quiver varieties, whose A-theory admits an AHa0C-action. These triples can be interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action of AHa0C on the cohomology of Hilbert schemes of points on T∗C. article_number: '30' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sasha full_name: Minets, Sasha id: 3E7C5304-F248-11E8-B48F-1D18A9856A87 last_name: Minets orcid: 0000-0003-3883-1806 citation: ama: Minets S. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 2020;26(2). doi:10.1007/s00029-020-00553-x apa: Minets, S. (2020). Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. Springer Nature. https://doi.org/10.1007/s00029-020-00553-x chicago: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series. Springer Nature, 2020. https://doi.org/10.1007/s00029-020-00553-x. ieee: S. Minets, “Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces,” Selecta Mathematica, New Series, vol. 26, no. 2. Springer Nature, 2020. ista: Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2), 30. mla: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series, vol. 26, no. 2, 30, Springer Nature, 2020, doi:10.1007/s00029-020-00553-x. short: S. Minets, Selecta Mathematica, New Series 26 (2020). date_created: 2020-04-26T22:00:44Z date_published: 2020-04-15T00:00:00Z date_updated: 2023-08-21T06:14:58Z day: '15' ddc: - '510' department: - _id: TaHa doi: 10.1007/s00029-020-00553-x external_id: arxiv: - '1801.01429' isi: - '000526036400001' file: - access_level: open_access checksum: 2368c4662629b4759295eb365323b2ad content_type: application/pdf creator: dernst date_created: 2020-04-28T10:57:58Z date_updated: 2020-07-14T12:48:02Z file_id: '7690' file_name: 2020_SelectaMathematica_Minets.pdf file_size: 792469 relation: main_file file_date_updated: 2020-07-14T12:48:02Z has_accepted_license: '1' intvolume: ' 26' isi: 1 issue: '2' language: - iso: eng month: '04' oa: 1 oa_version: Published Version project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Selecta Mathematica, New Series publication_identifier: eissn: - '14209020' issn: - '10221824' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 26 year: '2020' ... --- _id: '7940' abstract: - lang: eng text: We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay, Regelskis, and Wendlandt [GRW18]. acknowledgement: Gufang Zhao is affiliated to IST Austria, Hausel group until July of 2018. Supported by the Advanced Grant Arithmetic and Physics of Higgs moduli spaces No. 320593 of the European Research Council. article_processing_charge: No article_type: original author: - first_name: Yaping full_name: Yang, Yaping id: 360D8648-F248-11E8-B48F-1D18A9856A87 last_name: Yang - first_name: Gufang full_name: Zhao, Gufang id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87 last_name: Zhao citation: ama: Yang Y, Zhao G. The PBW theorem for affine Yangians. Transformation Groups. 2020;25:1371-1385. doi:10.1007/s00031-020-09572-6 apa: Yang, Y., & Zhao, G. (2020). The PBW theorem for affine Yangians. Transformation Groups. Springer Nature. https://doi.org/10.1007/s00031-020-09572-6 chicago: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” Transformation Groups. Springer Nature, 2020. https://doi.org/10.1007/s00031-020-09572-6. ieee: Y. Yang and G. Zhao, “The PBW theorem for affine Yangians,” Transformation Groups, vol. 25. Springer Nature, pp. 1371–1385, 2020. ista: Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation Groups. 25, 1371–1385. mla: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” Transformation Groups, vol. 25, Springer Nature, 2020, pp. 1371–85, doi:10.1007/s00031-020-09572-6. short: Y. Yang, G. Zhao, Transformation Groups 25 (2020) 1371–1385. date_created: 2020-06-07T22:00:55Z date_published: 2020-12-01T00:00:00Z date_updated: 2023-08-21T07:06:21Z day: '01' department: - _id: TaHa doi: 10.1007/s00031-020-09572-6 ec_funded: 1 external_id: arxiv: - '1804.04375' isi: - '000534874300003' intvolume: ' 25' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1804.04375 month: '12' oa: 1 oa_version: Preprint page: 1371-1385 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Transformation Groups publication_identifier: eissn: - 1531586X issn: - '10834362' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The PBW theorem for affine Yangians type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 25 year: '2020' ... --- _id: '8325' abstract: - lang: eng text: "Let \U0001D439:ℤ2→ℤ be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes. " acknowledgement: We thank Andrea Sportiello for sharing his insights on perturbative regimes of the Abelian sandpile model which was the starting point of our work. We also thank Grigory Mikhalkin, who encouraged us to approach this problem. We thank an anonymous referee. Also we thank Misha Khristoforov and Sergey Lanzat who participated on the initial state of this project, when we had nothing except the computer simulation and pictures. We thank Mikhail Raskin for providing us the code on Golly for faster simulations. Ilia Zharkov, Ilia Itenberg, Kristin Shaw, Max Karev, Lionel Levine, Ernesto Lupercio, Pavol Ševera, Yulieth Prieto, Michael Polyak, Danila Cherkashin asked us a lot of questions and listened to us; not all of their questions found answers here, but we are going to treat them in subsequent papers. article_processing_charge: No article_type: original author: - first_name: Nikita full_name: Kalinin, Nikita last_name: Kalinin - first_name: Mikhail full_name: Shkolnikov, Mikhail id: 35084A62-F248-11E8-B48F-1D18A9856A87 last_name: Shkolnikov orcid: 0000-0002-4310-178X citation: ama: Kalinin N, Shkolnikov M. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 2020;378(9):1649-1675. doi:10.1007/s00220-020-03828-8 apa: Kalinin, N., & Shkolnikov, M. (2020). Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-020-03828-8 chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-020-03828-8. ieee: N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic functions,” Communications in Mathematical Physics, vol. 378, no. 9. Springer Nature, pp. 1649–1675, 2020. ista: Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 378(9), 1649–1675. mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” Communications in Mathematical Physics, vol. 378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:10.1007/s00220-020-03828-8. short: N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020) 1649–1675. date_created: 2020-08-30T22:01:13Z date_published: 2020-09-01T00:00:00Z date_updated: 2023-08-22T09:00:03Z day: '01' department: - _id: TaHa doi: 10.1007/s00220-020-03828-8 ec_funded: 1 external_id: arxiv: - '1711.04285' isi: - '000560620600001' intvolume: ' 378' isi: 1 issue: '9' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1711.04285 month: '09' oa: 1 oa_version: Preprint page: 1649-1675 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Communications in Mathematical Physics publication_identifier: eissn: - '14320916' issn: - '00103616' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Sandpile solitons via smoothing of superharmonic functions type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 378 year: '2020' ... --- _id: '8539' abstract: - lang: eng text: Cohomological and K-theoretic stable bases originated from the study of quantum cohomology and quantum K-theory. Restriction formula for cohomological stable bases played an important role in computing the quantum connection of cotangent bundle of partial flag varieties. In this paper we study the K-theoretic stable bases of cotangent bundles of flag varieties. We describe these bases in terms of the action of the affine Hecke algebra and the twisted group algebra of KostantKumar. Using this algebraic description and the method of root polynomials, we give a restriction formula of the stable bases. We apply it to obtain the restriction formula for partial flag varieties. We also build a relation between the stable basis and the Casselman basis in the principal series representations of the Langlands dual group. As an application, we give a closed formula for the transition matrix between Casselman basis and the characteristic functions. - lang: fre text: "Les bases stables cohomologiques et K-théoriques proviennent de l’étude de la cohomologie quantique et de la K-théorie quantique. La formule de restriction pour les bases stables cohomologiques a joué un rôle important dans le calcul de la connexion quantique du fibré cotangent de variétés de drapeaux partielles. Dans cet article, nous étudions les bases stables K-théoriques de fibré cotangents des variétés de drapeaux. Nous décrivons ces bases en fonction de l’action de l’algèbre de Hecke affine et de l’algèbre de Kostant-Kumar. En utilisant cette description algébrique et la méthode des polynômes de racine, nous donnons une formule de restriction des bases stables. Nous l’appliquons\r\npour obtenir la formule de restriction pour les variétés de drapeaux partielles. Nous construisons également une relation entre la base stable et la base de Casselman dans les représentations de la série principale du groupe dual de Langlands p-adique. Comme une application, nous donnons une formule close pour la matrice de transition entre la base de Casselman et les fonctions caractéristiques. " article_processing_charge: No article_type: original author: - first_name: C. full_name: Su, C. last_name: Su - first_name: Gufang full_name: Zhao, Gufang id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87 last_name: Zhao - first_name: C. full_name: Zhong, C. last_name: Zhong citation: ama: Su C, Zhao G, Zhong C. On the K-theory stable bases of the springer resolution. Annales Scientifiques de l’Ecole Normale Superieure. 2020;53(3):663-671. doi:10.24033/asens.2431 apa: Su, C., Zhao, G., & Zhong, C. (2020). On the K-theory stable bases of the springer resolution. Annales Scientifiques de l’Ecole Normale Superieure. Société Mathématique de France. https://doi.org/10.24033/asens.2431 chicago: Su, C., Gufang Zhao, and C. Zhong. “On the K-Theory Stable Bases of the Springer Resolution.” Annales Scientifiques de l’Ecole Normale Superieure. Société Mathématique de France, 2020. https://doi.org/10.24033/asens.2431. ieee: C. Su, G. Zhao, and C. Zhong, “On the K-theory stable bases of the springer resolution,” Annales Scientifiques de l’Ecole Normale Superieure, vol. 53, no. 3. Société Mathématique de France, pp. 663–671, 2020. ista: Su C, Zhao G, Zhong C. 2020. On the K-theory stable bases of the springer resolution. Annales Scientifiques de l’Ecole Normale Superieure. 53(3), 663–671. mla: Su, C., et al. “On the K-Theory Stable Bases of the Springer Resolution.” Annales Scientifiques de l’Ecole Normale Superieure, vol. 53, no. 3, Société Mathématique de France, 2020, pp. 663–71, doi:10.24033/asens.2431. short: C. Su, G. Zhao, C. Zhong, Annales Scientifiques de l’Ecole Normale Superieure 53 (2020) 663–671. date_created: 2020-09-20T22:01:38Z date_published: 2020-06-01T00:00:00Z date_updated: 2023-08-22T09:27:57Z day: '01' department: - _id: TaHa doi: 10.24033/asens.2431 external_id: arxiv: - '1708.08013' isi: - '000592182600004' intvolume: ' 53' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.08013 month: '06' oa: 1 oa_version: Preprint page: 663-671 publication: Annales Scientifiques de l'Ecole Normale Superieure publication_identifier: issn: - 0012-9593 publication_status: published publisher: Société Mathématique de France quality_controlled: '1' scopus_import: '1' status: public title: On the K-theory stable bases of the springer resolution type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 53 year: '2020' ... --- _id: '15070' abstract: - lang: eng text: This workshop focused on interactions between the various perspectives on the moduli space of Higgs bundles over a Riemann surface. This subject draws on algebraic geometry, geometric topology, geometric analysis and mathematical physics, and the goal was to promote interactions between these various branches of the subject. The main current directions of research were well represented by the participants, and the talks included many from both senior and junior participants. article_processing_charge: No article_type: original author: - first_name: Lara full_name: Anderson, Lara last_name: Anderson - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Rafe full_name: Mazzeo, Rafe last_name: Mazzeo - first_name: Laura full_name: Schaposnik, Laura last_name: Schaposnik citation: ama: Anderson L, Hausel T, Mazzeo R, Schaposnik L. Geometry and physics of Higgs bundles. Oberwolfach Reports. 2020;16(2):1357-1417. doi:10.4171/owr/2019/23 apa: Anderson, L., Hausel, T., Mazzeo, R., & Schaposnik, L. (2020). Geometry and physics of Higgs bundles. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/23 chicago: Anderson, Lara, Tamás Hausel, Rafe Mazzeo, and Laura Schaposnik. “Geometry and Physics of Higgs Bundles.” Oberwolfach Reports. European Mathematical Society, 2020. https://doi.org/10.4171/owr/2019/23. ieee: L. Anderson, T. Hausel, R. Mazzeo, and L. Schaposnik, “Geometry and physics of Higgs bundles,” Oberwolfach Reports, vol. 16, no. 2. European Mathematical Society, pp. 1357–1417, 2020. ista: Anderson L, Hausel T, Mazzeo R, Schaposnik L. 2020. Geometry and physics of Higgs bundles. Oberwolfach Reports. 16(2), 1357–1417. mla: Anderson, Lara, et al. “Geometry and Physics of Higgs Bundles.” Oberwolfach Reports, vol. 16, no. 2, European Mathematical Society, 2020, pp. 1357–417, doi:10.4171/owr/2019/23. short: L. Anderson, T. Hausel, R. Mazzeo, L. Schaposnik, Oberwolfach Reports 16 (2020) 1357–1417. date_created: 2024-03-04T11:36:31Z date_published: 2020-06-04T00:00:00Z date_updated: 2024-03-11T09:20:34Z day: '04' department: - _id: TaHa doi: 10.4171/owr/2019/23 intvolume: ' 16' issue: '2' keyword: - Organic Chemistry - Biochemistry language: - iso: eng month: '06' oa_version: None page: 1357-1417 publication: Oberwolfach Reports publication_identifier: issn: - 1660-8933 publication_status: published publisher: European Mathematical Society quality_controlled: '1' status: public title: Geometry and physics of Higgs bundles type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2020' ... --- _id: '441' article_processing_charge: No article_type: original author: - first_name: Nikita full_name: Kalinin, Nikita last_name: Kalinin - first_name: Mikhail full_name: Shkolnikov, Mikhail id: 35084A62-F248-11E8-B48F-1D18A9856A87 last_name: Shkolnikov orcid: 0000-0002-4310-178X citation: ama: Kalinin N, Shkolnikov M. Tropical formulae for summation over a part of SL(2,Z). European Journal of Mathematics. 2019;5(3):909–928. doi:10.1007/s40879-018-0218-0 apa: Kalinin, N., & Shkolnikov, M. (2019). Tropical formulae for summation over a part of SL(2,Z). European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-018-0218-0 chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Tropical Formulae for Summation over a Part of SL(2,Z).” European Journal of Mathematics. Springer Nature, 2019. https://doi.org/10.1007/s40879-018-0218-0. ieee: N. Kalinin and M. Shkolnikov, “Tropical formulae for summation over a part of SL(2,Z),” European Journal of Mathematics, vol. 5, no. 3. Springer Nature, pp. 909–928, 2019. ista: Kalinin N, Shkolnikov M. 2019. Tropical formulae for summation over a part of SL(2,Z). European Journal of Mathematics. 5(3), 909–928. mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Tropical Formulae for Summation over a Part of SL(2,Z).” European Journal of Mathematics, vol. 5, no. 3, Springer Nature, 2019, pp. 909–928, doi:10.1007/s40879-018-0218-0. short: N. Kalinin, M. Shkolnikov, European Journal of Mathematics 5 (2019) 909–928. date_created: 2018-12-11T11:46:29Z date_published: 2019-09-15T00:00:00Z date_updated: 2021-01-12T07:56:46Z day: '15' department: - _id: TaHa doi: 10.1007/s40879-018-0218-0 ec_funded: 1 external_id: arxiv: - '1711.02089' intvolume: ' 5' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1711.02089 month: '09' oa: 1 oa_version: Preprint page: 909–928 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: European Journal of Mathematics publication_identifier: eissn: - 2199-6768 issn: - 2199-675X publication_status: published publisher: Springer Nature publist_id: '7382' quality_controlled: '1' scopus_import: 1 status: public title: Tropical formulae for summation over a part of SL(2,Z) type: journal_article user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 5 year: '2019' ... --- _id: '439' abstract: - lang: eng text: "We count points over a finite field on wild character varieties,of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras. Our result leads to the conjecture that the mixed Hodge polynomials of these character varieties agree with previously conjectured perverse Hodge polynomials of certain twisted parabolic Higgs moduli spaces, indicating the\r\npossibility of a P = W conjecture for a suitable wild Hitchin system." article_processing_charge: No article_type: original author: - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Martin full_name: Mereb, Martin id: 43D735EE-F248-11E8-B48F-1D18A9856A87 last_name: Mereb - first_name: Michael full_name: Wong, Michael last_name: Wong citation: ama: Hausel T, Mereb M, Wong M. Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. 2019;21(10):2995-3052. doi:10.4171/JEMS/896 apa: Hausel, T., Mereb, M., & Wong, M. (2019). Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/896 chicago: Hausel, Tamás, Martin Mereb, and Michael Wong. “Arithmetic and Representation Theory of Wild Character Varieties.” Journal of the European Mathematical Society. European Mathematical Society, 2019. https://doi.org/10.4171/JEMS/896. ieee: T. Hausel, M. Mereb, and M. Wong, “Arithmetic and representation theory of wild character varieties,” Journal of the European Mathematical Society, vol. 21, no. 10. European Mathematical Society, pp. 2995–3052, 2019. ista: Hausel T, Mereb M, Wong M. 2019. Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. 21(10), 2995–3052. mla: Hausel, Tamás, et al. “Arithmetic and Representation Theory of Wild Character Varieties.” Journal of the European Mathematical Society, vol. 21, no. 10, European Mathematical Society, 2019, pp. 2995–3052, doi:10.4171/JEMS/896. short: T. Hausel, M. Mereb, M. Wong, Journal of the European Mathematical Society 21 (2019) 2995–3052. date_created: 2018-12-11T11:46:29Z date_published: 2019-10-01T00:00:00Z date_updated: 2023-08-24T14:24:49Z day: '01' department: - _id: TaHa doi: 10.4171/JEMS/896 ec_funded: 1 external_id: arxiv: - '1604.03382' isi: - '000480413600002' intvolume: ' 21' isi: 1 issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1604.03382 month: '10' oa: 1 oa_version: Preprint page: 2995-3052 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Journal of the European Mathematical Society publication_identifier: eissn: - 1435-9855 publication_status: published publisher: European Mathematical Society publist_id: '7384' quality_controlled: '1' scopus_import: '1' status: public title: Arithmetic and representation theory of wild character varieties type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 21 year: '2019' ... --- _id: '6986' abstract: - lang: eng text: 'Li-Nadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti geometric Langlands conjecture of Ben-Zvi-Nadler in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds in the natural generality of reflection groups in Euclidean or hyperbolic space. As a corollary, we give an expression of the centralizer of a finite order element in a reflection group using homotopy theory. ' article_processing_charge: No article_type: original author: - first_name: Penghui full_name: Li, Penghui id: 42A24CCC-F248-11E8-B48F-1D18A9856A87 last_name: Li citation: ama: Li P. A colimit of traces of reflection groups. Proceedings of the American Mathematical Society. 2019;147(11):4597-4604. doi:10.1090/proc/14586 apa: Li, P. (2019). A colimit of traces of reflection groups. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14586 chicago: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14586. ieee: P. Li, “A colimit of traces of reflection groups,” Proceedings of the American Mathematical Society, vol. 147, no. 11. AMS, pp. 4597–4604, 2019. ista: Li P. 2019. A colimit of traces of reflection groups. Proceedings of the American Mathematical Society. 147(11), 4597–4604. mla: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings of the American Mathematical Society, vol. 147, no. 11, AMS, 2019, pp. 4597–604, doi:10.1090/proc/14586. short: P. Li, Proceedings of the American Mathematical Society 147 (2019) 4597–4604. date_created: 2019-11-04T16:10:50Z date_published: 2019-11-01T00:00:00Z date_updated: 2023-09-05T12:22:21Z day: '01' department: - _id: TaHa doi: 10.1090/proc/14586 ec_funded: 1 external_id: arxiv: - '1810.07039' isi: - '000488621700004' intvolume: ' 147' isi: 1 issue: '11' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1810.07039 month: '11' oa: 1 oa_version: Preprint page: 4597-4604 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Proceedings of the American Mathematical Society publication_identifier: eissn: - 1088-6826 issn: - 0002-9939 publication_status: published publisher: AMS quality_controlled: '1' scopus_import: '1' status: public title: A colimit of traces of reflection groups type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 147 year: '2019' ... --- _id: '196' abstract: - lang: eng text: 'The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit is subject of extensive collaborative research. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second and third order harmonics resemble smooth stretchings, respectively translations, of the identity, while the ones induced by fourth order harmonics resemble magnifications and rotations. Starting with order three, the dynamics pass through extended regions of seemingly random configurations which spontaneously reassemble into accentuated patterns. We show that the space of harmonic functions projects to the extended analogue of the sandpile group, thus providing a set of universal coordinates identifying configurations between different domains. Since the original sandpile group is a subgroup of the extended one, this directly implies that it admits a natural renormalization. Furthermore, we show that the harmonic fields can be induced by simple Markov processes, and that the corresponding stochastic dynamics show remarkable robustness over hundreds of periods. Finally, we encode information into seemingly random configurations, and decode this information with an algorithm requiring minimal prior knowledge. Our results suggest that harmonic fields might split the sandpile group into sub-sets showing different critical coefficients, and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain. ' acknowledgement: "M.L. is grateful to the members of the C Guet and G Tkacik groups for valuable comments and support. M.S. is grateful to Nikita Kalinin for inspiring communications.\r\n" article_processing_charge: No article_type: original author: - first_name: Moritz full_name: Lang, Moritz id: 29E0800A-F248-11E8-B48F-1D18A9856A87 last_name: Lang - first_name: Mikhail full_name: Shkolnikov, Mikhail id: 35084A62-F248-11E8-B48F-1D18A9856A87 last_name: Shkolnikov orcid: 0000-0002-4310-178X citation: ama: Lang M, Shkolnikov M. Harmonic dynamics of the Abelian sandpile. Proceedings of the National Academy of Sciences. 2019;116(8):2821-2830. doi:10.1073/pnas.1812015116 apa: Lang, M., & Shkolnikov, M. (2019). Harmonic dynamics of the Abelian sandpile. Proceedings of the National Academy of Sciences. National Academy of Sciences. https://doi.org/10.1073/pnas.1812015116 chicago: Lang, Moritz, and Mikhail Shkolnikov. “Harmonic Dynamics of the Abelian Sandpile.” Proceedings of the National Academy of Sciences. National Academy of Sciences, 2019. https://doi.org/10.1073/pnas.1812015116. ieee: M. Lang and M. Shkolnikov, “Harmonic dynamics of the Abelian sandpile,” Proceedings of the National Academy of Sciences, vol. 116, no. 8. National Academy of Sciences, pp. 2821–2830, 2019. ista: Lang M, Shkolnikov M. 2019. Harmonic dynamics of the Abelian sandpile. Proceedings of the National Academy of Sciences. 116(8), 2821–2830. mla: Lang, Moritz, and Mikhail Shkolnikov. “Harmonic Dynamics of the Abelian Sandpile.” Proceedings of the National Academy of Sciences, vol. 116, no. 8, National Academy of Sciences, 2019, pp. 2821–30, doi:10.1073/pnas.1812015116. short: M. Lang, M. Shkolnikov, Proceedings of the National Academy of Sciences 116 (2019) 2821–2830. date_created: 2018-12-11T11:45:08Z date_published: 2019-02-19T00:00:00Z date_updated: 2023-09-11T14:09:34Z day: '19' department: - _id: CaGu - _id: GaTk - _id: TaHa doi: 10.1073/pnas.1812015116 external_id: arxiv: - '1806.10823' isi: - '000459074400013' pmid: - ' 30728300' intvolume: ' 116' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1073/pnas.1812015116 month: '02' oa: 1 oa_version: Published Version page: 2821-2830 pmid: 1 publication: Proceedings of the National Academy of Sciences publication_identifier: eissn: - 1091-6490 publication_status: published publisher: National Academy of Sciences quality_controlled: '1' related_material: link: - description: News on IST Webpage relation: press_release url: https://ist.ac.at/en/news/famous-sandpile-model-shown-to-move-like-a-traveling-sand-dune/ scopus_import: '1' status: public title: Harmonic dynamics of the Abelian sandpile type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 116 year: '2019' ... --- _id: '5' abstract: - lang: eng text: In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup. In order to define the wonderful compactification for a quantum group, we adopt a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key to our construction is a quantum version of the Vinberg semigroup, which we define as a q-deformation of a certain Rees algebra, compatible with a standard Poisson structure. Furthermore, we discuss quantum analogues of the stratification of the wonderful compactification by orbits for a certain group action, and provide explicit computations in the case of SL2. article_processing_charge: Yes (via OA deal) author: - first_name: Iordan V full_name: Ganev, Iordan V id: 447491B8-F248-11E8-B48F-1D18A9856A87 last_name: Ganev citation: ama: Ganev IV. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. 2019;99(3):778-806. doi:10.1112/jlms.12193 apa: Ganev, I. V. (2019). The wonderful compactification for quantum groups. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12193 chicago: Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” Journal of the London Mathematical Society. Wiley, 2019. https://doi.org/10.1112/jlms.12193. ieee: I. V. Ganev, “The wonderful compactification for quantum groups,” Journal of the London Mathematical Society, vol. 99, no. 3. Wiley, pp. 778–806, 2019. ista: Ganev IV. 2019. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. 99(3), 778–806. mla: Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” Journal of the London Mathematical Society, vol. 99, no. 3, Wiley, 2019, pp. 778–806, doi:10.1112/jlms.12193. short: I.V. Ganev, Journal of the London Mathematical Society 99 (2019) 778–806. date_created: 2018-12-11T11:44:06Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-19T10:13:08Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1112/jlms.12193 external_id: isi: - '000470025900008' file: - access_level: open_access checksum: 1be56239b2cd740a0e9a084f773c22f6 content_type: application/pdf creator: kschuh date_created: 2020-01-07T13:31:53Z date_updated: 2020-07-14T12:46:35Z file_id: '7238' file_name: 2019_Wiley_Ganev.pdf file_size: 431754 relation: main_file file_date_updated: 2020-07-14T12:46:35Z has_accepted_license: '1' intvolume: ' 99' isi: 1 issue: '3' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 778-806 publication: Journal of the London Mathematical Society publication_status: published publisher: Wiley publist_id: '8052' quality_controlled: '1' scopus_import: '1' status: public title: The wonderful compactification for quantum groups tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 99 year: '2019' ... --- _id: '7436' abstract: - lang: eng text: 'For an ordinary K3 surface over an algebraically closed field of positive characteristic we show that every automorphism lifts to characteristic zero. Moreover, we show that the Fourier-Mukai partners of an ordinary K3 surface are in one-to-one correspondence with the Fourier-Mukai partners of the geometric generic fiber of its canonical lift. We also prove that the explicit counting formula for Fourier-Mukai partners of the K3 surfaces with Picard rank two and with discriminant equal to minus of a prime number, in terms of the class number of the prime, holds over a field of positive characteristic as well. We show that the image of the derived autoequivalence group of a K3 surface of finite height in the group of isometries of its crystalline cohomology has index at least two. Moreover, we provide a conditional upper bound on the kernel of this natural cohomological descent map. Further, we give an extended remark in the appendix on the possibility of an F-crystal structure on the crystalline cohomology of a K3 surface over an algebraically closed field of positive characteristic and show that the naive F-crystal structure fails in being compatible with inner product. ' article_processing_charge: No article_type: original author: - first_name: Tanya K full_name: Srivastava, Tanya K id: 4D046628-F248-11E8-B48F-1D18A9856A87 last_name: Srivastava citation: ama: Srivastava TK. On derived equivalences of k3 surfaces in positive characteristic. Documenta Mathematica. 2019;24:1135-1177. doi:10.25537/dm.2019v24.1135-1177 apa: Srivastava, T. K. (2019). On derived equivalences of k3 surfaces in positive characteristic. Documenta Mathematica. EMS Press. https://doi.org/10.25537/dm.2019v24.1135-1177 chicago: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.” Documenta Mathematica. EMS Press, 2019. https://doi.org/10.25537/dm.2019v24.1135-1177. ieee: T. K. Srivastava, “On derived equivalences of k3 surfaces in positive characteristic,” Documenta Mathematica, vol. 24. EMS Press, pp. 1135–1177, 2019. ista: Srivastava TK. 2019. On derived equivalences of k3 surfaces in positive characteristic. Documenta Mathematica. 24, 1135–1177. mla: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.” Documenta Mathematica, vol. 24, EMS Press, 2019, pp. 1135–77, doi:10.25537/dm.2019v24.1135-1177. short: T.K. Srivastava, Documenta Mathematica 24 (2019) 1135–1177. date_created: 2020-02-02T23:01:06Z date_published: 2019-05-20T00:00:00Z date_updated: 2023-10-17T07:42:21Z day: '20' ddc: - '510' department: - _id: TaHa doi: 10.25537/dm.2019v24.1135-1177 external_id: arxiv: - '1809.08970' isi: - '000517806400019' file: - access_level: open_access checksum: 9a1a64bd49ab03fa4f738fb250fc4f90 content_type: application/pdf creator: dernst date_created: 2020-02-03T06:26:12Z date_updated: 2020-07-14T12:47:58Z file_id: '7438' file_name: 2019_DocumMath_Srivastava.pdf file_size: 469730 relation: main_file file_date_updated: 2020-07-14T12:47:58Z has_accepted_license: '1' intvolume: ' 24' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 1135-1177 publication: Documenta Mathematica publication_identifier: eissn: - 1431-0643 issn: - 1431-0635 publication_status: published publisher: EMS Press quality_controlled: '1' scopus_import: '1' status: public title: On derived equivalences of k3 surfaces in positive characteristic tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2019' ... --- _id: '61' abstract: - lang: eng text: 'We prove that there is no strongly regular graph (SRG) with parameters (460; 153; 32; 60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs. ' article_processing_charge: No author: - first_name: Andriy full_name: Bondarenko, Andriy last_name: Bondarenko - first_name: Anton full_name: Mellit, Anton id: 388D3134-F248-11E8-B48F-1D18A9856A87 last_name: Mellit - first_name: Andriy full_name: Prymak, Andriy last_name: Prymak - first_name: Danylo full_name: Radchenko, Danylo last_name: Radchenko - first_name: Maryna full_name: Viazovska, Maryna last_name: Viazovska citation: ama: 'Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. There is no strongly regular graph with parameters (460; 153; 32; 60). In: Contemporary Computational Mathematics. Springer; 2018:131-134. doi:10.1007/978-3-319-72456-0_7' apa: Bondarenko, A., Mellit, A., Prymak, A., Radchenko, D., & Viazovska, M. (2018). There is no strongly regular graph with parameters (460; 153; 32; 60). In Contemporary Computational Mathematics (pp. 131–134). Springer. https://doi.org/10.1007/978-3-319-72456-0_7 chicago: Bondarenko, Andriy, Anton Mellit, Andriy Prymak, Danylo Radchenko, and Maryna Viazovska. “There Is No Strongly Regular Graph with Parameters (460; 153; 32; 60).” In Contemporary Computational Mathematics, 131–34. Springer, 2018. https://doi.org/10.1007/978-3-319-72456-0_7. ieee: A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, and M. Viazovska, “There is no strongly regular graph with parameters (460; 153; 32; 60),” in Contemporary Computational Mathematics, Springer, 2018, pp. 131–134. ista: 'Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. 2018.There is no strongly regular graph with parameters (460; 153; 32; 60). In: Contemporary Computational Mathematics. , 131–134.' mla: Bondarenko, Andriy, et al. “There Is No Strongly Regular Graph with Parameters (460; 153; 32; 60).” Contemporary Computational Mathematics, Springer, 2018, pp. 131–34, doi:10.1007/978-3-319-72456-0_7. short: A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, M. Viazovska, in:, Contemporary Computational Mathematics, Springer, 2018, pp. 131–134. date_created: 2018-12-11T11:44:25Z date_published: 2018-05-23T00:00:00Z date_updated: 2021-01-12T08:06:06Z day: '23' department: - _id: TaHa doi: 10.1007/978-3-319-72456-0_7 extern: '1' external_id: arxiv: - '1509.06286' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1509.06286 month: '05' oa: 1 oa_version: Preprint page: 131 - 134 publication: Contemporary Computational Mathematics publication_status: published publisher: Springer publist_id: '7993' quality_controlled: '1' status: public title: There is no strongly regular graph with parameters (460; 153; 32; 60) type: book_chapter user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2018' ... --- _id: '6525' abstract: - lang: eng text: This chapter finds an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL2 Higgs moduli space on a Riemann surface. On one side of the agreement, components of the Lagrangian brane of U(1,1) Higgs bundles, whose mirror was proposed by Hitchin to be certain even exterior powers of the hyperholomorphic Dirac bundle on the SL2 Higgs moduli space, are present. The agreement arises from a mysterious functional equation. This gives strong computational evidence for Hitchin’s proposal. author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Anton full_name: Mellit, Anton id: 388D3134-F248-11E8-B48F-1D18A9856A87 last_name: Mellit - first_name: Du full_name: Pei, Du last_name: Pei citation: ama: 'Hausel T, Mellit A, Pei D. Mirror symmetry with branes by equivariant verlinde formulas. In: Geometry and Physics: Volume I. Oxford University Press; 2018:189-218. doi:10.1093/oso/9780198802013.003.0009' apa: 'Hausel, T., Mellit, A., & Pei, D. (2018). Mirror symmetry with branes by equivariant verlinde formulas. In Geometry and Physics: Volume I (pp. 189–218). Oxford University Press. https://doi.org/10.1093/oso/9780198802013.003.0009' chicago: 'Hausel, Tamás, Anton Mellit, and Du Pei. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” In Geometry and Physics: Volume I, 189–218. Oxford University Press, 2018. https://doi.org/10.1093/oso/9780198802013.003.0009.' ieee: 'T. Hausel, A. Mellit, and D. Pei, “Mirror symmetry with branes by equivariant verlinde formulas,” in Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218.' ista: 'Hausel T, Mellit A, Pei D. 2018.Mirror symmetry with branes by equivariant verlinde formulas. In: Geometry and Physics: Volume I. , 189–218.' mla: 'Hausel, Tamás, et al. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218, doi:10.1093/oso/9780198802013.003.0009.' short: 'T. Hausel, A. Mellit, D. Pei, in:, Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218.' date_created: 2019-06-06T12:42:01Z date_published: 2018-01-01T00:00:00Z date_updated: 2021-01-12T08:07:52Z day: '01' department: - _id: TaHa doi: 10.1093/oso/9780198802013.003.0009 language: - iso: eng month: '01' oa_version: None page: 189-218 publication: 'Geometry and Physics: Volume I' publication_identifier: isbn: - '9780198802013' - '9780191840500' publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: 1 status: public title: Mirror symmetry with branes by equivariant verlinde formulas type: book_chapter user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2018' ... --- _id: '303' abstract: - lang: eng text: The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results we need for other articles and also introduces several objects interesting by themselves. acknowledgement: The first author, Nikita Kalinin, is funded by SNCF PostDoc.Mobility grant 168647. Support from the Basic Research Program of the National Research University Higher School of Economics is gratefully acknowledged. The second author, Mikhail Shkolnikov, is supported in part by the grant 159240 of the Swiss National Science Foundation as well as by the National Center of Competence in Research SwissMAP of the Swiss National Science Foundation. article_processing_charge: No author: - first_name: Nikita full_name: Kalinin, Nikita last_name: Kalinin - first_name: Mikhail full_name: Shkolnikov, Mikhail id: 35084A62-F248-11E8-B48F-1D18A9856A87 last_name: Shkolnikov orcid: 0000-0002-4310-178X citation: ama: Kalinin N, Shkolnikov M. Introduction to tropical series and wave dynamic on them. Discrete and Continuous Dynamical Systems- Series A. 2018;38(6):2827-2849. doi:10.3934/dcds.2018120 apa: Kalinin, N., & Shkolnikov, M. (2018). Introduction to tropical series and wave dynamic on them. Discrete and Continuous Dynamical Systems- Series A. AIMS. https://doi.org/10.3934/dcds.2018120 chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and Wave Dynamic on Them.” Discrete and Continuous Dynamical Systems- Series A. AIMS, 2018. https://doi.org/10.3934/dcds.2018120. ieee: N. Kalinin and M. Shkolnikov, “Introduction to tropical series and wave dynamic on them,” Discrete and Continuous Dynamical Systems- Series A, vol. 38, no. 6. AIMS, pp. 2827–2849, 2018. ista: Kalinin N, Shkolnikov M. 2018. Introduction to tropical series and wave dynamic on them. Discrete and Continuous Dynamical Systems- Series A. 38(6), 2827–2849. mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and Wave Dynamic on Them.” Discrete and Continuous Dynamical Systems- Series A, vol. 38, no. 6, AIMS, 2018, pp. 2827–49, doi:10.3934/dcds.2018120. short: N. Kalinin, M. Shkolnikov, Discrete and Continuous Dynamical Systems- Series A 38 (2018) 2827–2849. date_created: 2018-12-11T11:45:43Z date_published: 2018-06-01T00:00:00Z date_updated: 2023-09-12T07:45:37Z day: '01' department: - _id: TaHa doi: 10.3934/dcds.2018120 external_id: arxiv: - '1706.03062' isi: - '000438818400007' intvolume: ' 38' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1706.03062 month: '06' oa: 1 oa_version: Submitted Version page: 2827 - 2849 publication: Discrete and Continuous Dynamical Systems- Series A publication_status: published publisher: AIMS publist_id: '7576' quality_controlled: '1' scopus_import: '1' status: public title: Introduction to tropical series and wave dynamic on them type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 38 year: '2018' ... --- _id: '322' abstract: - lang: eng text: We construct quantizations of multiplicative hypertoric varieties using an algebra of q-difference operators on affine space, where q is a root of unity in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the multiplicative hypertoric variety and admits an explicit finite étale splitting. The global sections of this Azumaya algebra is a hypertoric quantum group, and we prove a localization theorem. We introduce a general framework of Frobenius quantum moment maps and their Hamiltonian reductions; our results shed light on an instance of this framework. acknowledgement: "National Science Foundation: Graduate Research Fellowship and grant No.0932078000; ERC Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 \r\nThe author is grateful to David Jordan for suggesting this project and providing guidance throughout, particularly for the formulation of Frobenius quantum moment maps and key ideas in the proofs of Theorems 3.12 and 4.8. Special thanks to David Ben-Zvi (the author's PhD advisor) for numerous discussions and constant encouragement, and for suggesting the term ‘hypertoric quantum group.’ Many results appearing in the current paper were proven independently by Nicholas Cooney; the author is grateful to Nicholas for sharing his insight on various topics, including Proposition 3.8. The author also thanks Nicholas Proudfoot for relating the definition of multiplicative hypertoric varieties, as well as the content of Remark 2.14. The author also benefited immensely from the close reading and detailed comments of an anonymous referee, and from conversations with Justin Hilburn, Kobi Kremnitzer, Michael McBreen, Tom Nevins, Travis Schedler, and Ben Webster. \r\n\r\n\r\n\r\n" article_processing_charge: No author: - first_name: Iordan V full_name: Ganev, Iordan V id: 447491B8-F248-11E8-B48F-1D18A9856A87 last_name: Ganev citation: ama: Ganev IV. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 2018;506:92-128. doi:10.1016/j.jalgebra.2018.03.015 apa: Ganev, I. V. (2018). Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. World Scientific Publishing. https://doi.org/10.1016/j.jalgebra.2018.03.015 chicago: Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” Journal of Algebra. World Scientific Publishing, 2018. https://doi.org/10.1016/j.jalgebra.2018.03.015. ieee: I. V. Ganev, “Quantizations of multiplicative hypertoric varieties at a root of unity,” Journal of Algebra, vol. 506. World Scientific Publishing, pp. 92–128, 2018. ista: Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 506, 92–128. mla: Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” Journal of Algebra, vol. 506, World Scientific Publishing, 2018, pp. 92–128, doi:10.1016/j.jalgebra.2018.03.015. short: I.V. Ganev, Journal of Algebra 506 (2018) 92–128. date_created: 2018-12-11T11:45:49Z date_published: 2018-07-15T00:00:00Z date_updated: 2023-09-15T12:08:38Z day: '15' department: - _id: TaHa doi: 10.1016/j.jalgebra.2018.03.015 ec_funded: 1 external_id: arxiv: - '1412.7211' isi: - '000433270600005' intvolume: ' 506' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1412.7211 month: '07' oa: 1 oa_version: Preprint page: 92 - 128 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Journal of Algebra publication_status: published publisher: World Scientific Publishing publist_id: '7543' quality_controlled: '1' scopus_import: '1' status: public title: Quantizations of multiplicative hypertoric varieties at a root of unity type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 506 year: '2018' ... --- _id: '64' abstract: - lang: eng text: Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation. article_processing_charge: No article_type: original author: - first_name: Nikita full_name: Kalinin, Nikita last_name: Kalinin - first_name: Aldo full_name: Guzmán Sáenz, Aldo last_name: Guzmán Sáenz - first_name: Y full_name: Prieto, Y last_name: Prieto - first_name: Mikhail full_name: Shkolnikov, Mikhail id: 35084A62-F248-11E8-B48F-1D18A9856A87 last_name: Shkolnikov orcid: 0000-0002-4310-178X - first_name: V full_name: Kalinina, V last_name: Kalinina - first_name: Ernesto full_name: Lupercio, Ernesto last_name: Lupercio citation: ama: 'Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E. Self-organized criticality and pattern emergence through the lens of tropical geometry. PNAS: Proceedings of the National Academy of Sciences of the United States of America. 2018;115(35):E8135-E8142. doi:10.1073/pnas.1805847115' apa: 'Kalinin, N., Guzmán Sáenz, A., Prieto, Y., Shkolnikov, M., Kalinina, V., & Lupercio, E. (2018). Self-organized criticality and pattern emergence through the lens of tropical geometry. PNAS: Proceedings of the National Academy of Sciences of the United States of America. National Academy of Sciences. https://doi.org/10.1073/pnas.1805847115' chicago: 'Kalinin, Nikita, Aldo Guzmán Sáenz, Y Prieto, Mikhail Shkolnikov, V Kalinina, and Ernesto Lupercio. “Self-Organized Criticality and Pattern Emergence through the Lens of Tropical Geometry.” PNAS: Proceedings of the National Academy of Sciences of the United States of America. National Academy of Sciences, 2018. https://doi.org/10.1073/pnas.1805847115.' ieee: 'N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, and E. Lupercio, “Self-organized criticality and pattern emergence through the lens of tropical geometry,” PNAS: Proceedings of the National Academy of Sciences of the United States of America, vol. 115, no. 35. National Academy of Sciences, pp. E8135–E8142, 2018.' ista: 'Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E. 2018. Self-organized criticality and pattern emergence through the lens of tropical geometry. PNAS: Proceedings of the National Academy of Sciences of the United States of America. 115(35), E8135–E8142.' mla: 'Kalinin, Nikita, et al. “Self-Organized Criticality and Pattern Emergence through the Lens of Tropical Geometry.” PNAS: Proceedings of the National Academy of Sciences of the United States of America, vol. 115, no. 35, National Academy of Sciences, 2018, pp. E8135–42, doi:10.1073/pnas.1805847115.' short: 'N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, E. Lupercio, PNAS: Proceedings of the National Academy of Sciences of the United States of America 115 (2018) E8135–E8142.' date_created: 2018-12-11T11:44:26Z date_published: 2018-08-28T00:00:00Z date_updated: 2023-09-18T08:41:16Z day: '28' department: - _id: TaHa doi: 10.1073/pnas.1805847115 ec_funded: 1 external_id: arxiv: - '1806.09153' isi: - '000442861600009' intvolume: ' 115' isi: 1 issue: '35' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1806.09153 month: '08' oa: 1 oa_version: Preprint page: E8135 - E8142 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: 'PNAS: Proceedings of the National Academy of Sciences of the United States of America' publication_identifier: issn: - '00278424' publication_status: published publisher: National Academy of Sciences publist_id: '7990' quality_controlled: '1' scopus_import: '1' status: public title: Self-organized criticality and pattern emergence through the lens of tropical geometry type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 115 year: '2018' ... --- _id: '5999' abstract: - lang: eng text: "We introduce for each quiver Q and each algebraic oriented cohomology theory A, the cohomological Hall algebra (CoHA) of Q, as the A-homology of the moduli of representations of the preprojective algebra of Q. This generalizes the K-theoretic Hall algebra of commuting varieties defined by Schiffmann-Vasserot. When A is the Morava K-theory, we show evidence that this algebra is a candidate for Lusztig's reformulated conjecture on modular representations of algebraic groups.\r\nWe construct an action of the preprojective CoHA on the A-homology of Nakajima quiver varieties. We compare this with the action of the Borel subalgebra of Yangian when A is the intersection theory. We also give a shuffle algebra description of this CoHA in terms of the underlying formal group law of A. As applications, we obtain a shuffle description of the Yangian. " article_processing_charge: No author: - first_name: Yaping full_name: Yang, Yaping last_name: Yang - first_name: Gufang full_name: Zhao, Gufang id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87 last_name: Zhao citation: ama: Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 2018;116(5):1029-1074. doi:10.1112/plms.12111 apa: Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. Oxford University Press. https://doi.org/10.1112/plms.12111 chicago: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” Proceedings of the London Mathematical Society. Oxford University Press, 2018. https://doi.org/10.1112/plms.12111. ieee: Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,” Proceedings of the London Mathematical Society, vol. 116, no. 5. Oxford University Press, pp. 1029–1074, 2018. ista: Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 116(5), 1029–1074. mla: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” Proceedings of the London Mathematical Society, vol. 116, no. 5, Oxford University Press, 2018, pp. 1029–74, doi:10.1112/plms.12111. short: Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018) 1029–1074. date_created: 2019-02-14T13:14:22Z date_published: 2018-05-01T00:00:00Z date_updated: 2023-09-19T14:37:19Z day: '01' department: - _id: TaHa doi: 10.1112/plms.12111 external_id: arxiv: - '1407.7994' isi: - '000431506400001' intvolume: ' 116' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1407.7994 month: '05' oa: 1 oa_version: Preprint page: 1029-1074 publication: Proceedings of the London Mathematical Society publication_identifier: issn: - 0024-6115 publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: '1' status: public title: The cohomological Hall algebra of a preprojective algebra type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 116 year: '2018' ... --- _id: '687' abstract: - lang: eng text: Pursuing the similarity between the Kontsevich-Soibelman construction of the cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the integrality conjecture for motivic Donaldson-Thomas invariants and the PBW theorem for quantum enveloping algebras, we build a coproduct on the CoHA associated to a quiver with potential. We also prove a cohomological dimensional reduction theorem, further linking a special class of CoHAs with Yangians, and explaining how to connect the study of character varieties with the study of CoHAs. author: - first_name: Ben full_name: Davison, Ben id: 4634AB1E-F248-11E8-B48F-1D18A9856A87 last_name: Davison orcid: 0000-0002-8944-4390 citation: ama: Davison B. The critical CoHA of a quiver with potential. Quarterly Journal of Mathematics. 2017;68(2):635-703. doi:10.1093/qmath/haw053 apa: Davison, B. (2017). The critical CoHA of a quiver with potential. Quarterly Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qmath/haw053 chicago: Davison, Ben. “The Critical CoHA of a Quiver with Potential.” Quarterly Journal of Mathematics. Oxford University Press, 2017. https://doi.org/10.1093/qmath/haw053. ieee: B. Davison, “The critical CoHA of a quiver with potential,” Quarterly Journal of Mathematics, vol. 68, no. 2. Oxford University Press, pp. 635–703, 2017. ista: Davison B. 2017. The critical CoHA of a quiver with potential. Quarterly Journal of Mathematics. 68(2), 635–703. mla: Davison, Ben. “The Critical CoHA of a Quiver with Potential.” Quarterly Journal of Mathematics, vol. 68, no. 2, Oxford University Press, 2017, pp. 635–703, doi:10.1093/qmath/haw053. short: B. Davison, Quarterly Journal of Mathematics 68 (2017) 635–703. date_created: 2018-12-11T11:47:55Z date_published: 2017-06-01T00:00:00Z date_updated: 2021-01-12T08:09:24Z day: '01' department: - _id: TaHa doi: 10.1093/qmath/haw053 ec_funded: 1 intvolume: ' 68' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1311.7172 month: '06' oa: 1 oa_version: Submitted Version page: 635 - 703 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Quarterly Journal of Mathematics publication_identifier: issn: - '00335606' publication_status: published publisher: Oxford University Press publist_id: '7022' quality_controlled: '1' scopus_import: 1 status: public title: The critical CoHA of a quiver with potential type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 68 year: '2017' ...