[{"isi":1,"publication_status":"published","abstract":[{"text":"Let 𝐹: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. ","lang":"eng"}],"quality_controlled":"1","arxiv":1,"publication":"Communications in Mathematical Physics","publisher":"Springer Nature","language":[{"iso":"eng"}],"date_updated":"2025-07-10T11:57:03Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_created":"2020-08-30T22:01:13Z","doi":"10.1007/s00220-020-03828-8","_id":"8325","ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1711.04285"}],"article_type":"original","year":"2020","month":"09","day":"01","article_processing_charge":"No","status":"public","date_published":"2020-09-01T00:00:00Z","oa_version":"Preprint","volume":378,"type":"journal_article","author":[{"full_name":"Kalinin, Nikita","last_name":"Kalinin","first_name":"Nikita"},{"orcid":"0000-0002-4310-178X","full_name":"Shkolnikov, Mikhail","id":"35084A62-F248-11E8-B48F-1D18A9856A87","first_name":"Mikhail","last_name":"Shkolnikov"}],"department":[{"_id":"TaHa"}],"citation":{"ista":"Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 378(9), 1649–1675.","apa":"Kalinin, N., &#38; Shkolnikov, M. (2020). Sandpile solitons via smoothing of superharmonic functions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-020-03828-8\">https://doi.org/10.1007/s00220-020-03828-8</a>","chicago":"Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-020-03828-8\">https://doi.org/10.1007/s00220-020-03828-8</a>.","short":"N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020) 1649–1675.","mla":"Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:<a href=\"https://doi.org/10.1007/s00220-020-03828-8\">10.1007/s00220-020-03828-8</a>.","ieee":"N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic functions,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9. Springer Nature, pp. 1649–1675, 2020.","ama":"Kalinin N, Shkolnikov M. Sandpile solitons via smoothing of superharmonic functions. <i>Communications in Mathematical Physics</i>. 2020;378(9):1649-1675. doi:<a href=\"https://doi.org/10.1007/s00220-020-03828-8\">10.1007/s00220-020-03828-8</a>"},"project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7"}],"external_id":{"arxiv":["1711.04285"],"isi":["000560620600001"]},"page":"1649-1675","intvolume":"       378","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"title":"Sandpile solitons via smoothing of superharmonic functions","issue":"9","scopus_import":"1","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."},{"publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"publisher":"Springer Nature","date_updated":"2025-04-14T09:12:46Z","abstract":[{"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.","lang":"eng"}],"publication_status":"published","isi":1,"quality_controlled":"1","arxiv":1,"ec_funded":1,"_id":"7004","article_type":"original","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1810.10402"}],"year":"2020","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"date_created":"2019-11-12T14:01:27Z","doi":"10.1007/s00220-019-03575-5","volume":376,"author":[{"first_name":"Miroslav","last_name":"Rapcak","full_name":"Rapcak, Miroslav"},{"first_name":"Yan","last_name":"Soibelman","full_name":"Soibelman, Yan"},{"first_name":"Yaping","last_name":"Yang","full_name":"Yang, Yaping"},{"full_name":"Zhao, Gufang","first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","last_name":"Zhao"}],"type":"journal_article","citation":{"short":"M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical Physics 376 (2020) 1803–1873.","chicago":"Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03575-5\">https://doi.org/10.1007/s00220-019-03575-5</a>.","apa":"Rapcak, M., Soibelman, Y., Yang, Y., &#38; Zhao, G. (2020). Cohomological Hall algebras, vertex algebras and instantons. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03575-5\">https://doi.org/10.1007/s00220-019-03575-5</a>","ista":"Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873.","ama":"Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex algebras and instantons. <i>Communications in Mathematical Physics</i>. 2020;376:1803-1873. doi:<a href=\"https://doi.org/10.1007/s00220-019-03575-5\">10.1007/s00220-019-03575-5</a>","ieee":"M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras, vertex algebras and instantons,” <i>Communications in Mathematical Physics</i>, vol. 376. Springer Nature, pp. 1803–1873, 2020.","mla":"Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” <i>Communications in Mathematical Physics</i>, vol. 376, Springer Nature, 2020, pp. 1803–73, doi:<a href=\"https://doi.org/10.1007/s00220-019-03575-5\">10.1007/s00220-019-03575-5</a>."},"department":[{"_id":"TaHa"}],"day":"01","month":"06","status":"public","date_published":"2020-06-01T00:00:00Z","article_processing_charge":"No","oa_version":"Preprint","scopus_import":"1","external_id":{"isi":["000536255500004"],"arxiv":["1810.10402"]},"project":[{"call_identifier":"FP7","grant_number":"320593","_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces"}],"page":"1803-1873","intvolume":"       376","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"title":"Cohomological Hall algebras, vertex algebras and instantons"},{"publication":"Oberwolfach Reports","language":[{"iso":"eng"}],"publisher":"EMS Press","date_updated":"2026-07-06T11:52:54Z","publication_status":"published","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."}],"quality_controlled":"1","_id":"15070","article_type":"original","keyword":["Organic Chemistry","Biochemistry"],"year":"2020","das_tickbox":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2024-03-04T11:36:31Z","doi":"10.4171/owr/2019/23","volume":16,"type":"journal_article","author":[{"last_name":"Anderson","first_name":"Lara","full_name":"Anderson, Lara"},{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás","last_name":"Hausel","orcid":"0000-0002-9582-2634","full_name":"Hausel, Tamás"},{"last_name":"Mazzeo","first_name":"Rafe","full_name":"Mazzeo, Rafe"},{"first_name":"Laura","last_name":"Schaposnik","full_name":"Schaposnik, Laura"}],"citation":{"chicago":"Anderson, Lara, Tamás Hausel, Rafe Mazzeo, and Laura Schaposnik. “Geometry and Physics of Higgs Bundles.” <i>Oberwolfach Reports</i>. EMS Press, 2020. <a href=\"https://doi.org/10.4171/owr/2019/23\">https://doi.org/10.4171/owr/2019/23</a>.","short":"L. Anderson, T. Hausel, R. Mazzeo, L. Schaposnik, Oberwolfach Reports 16 (2020) 1357–1417.","ista":"Anderson L, Hausel T, Mazzeo R, Schaposnik L. 2020. Geometry and physics of Higgs bundles. Oberwolfach Reports. 16(2), 1357–1417.","apa":"Anderson, L., Hausel, T., Mazzeo, R., &#38; Schaposnik, L. (2020). Geometry and physics of Higgs bundles. <i>Oberwolfach Reports</i>. EMS Press. <a href=\"https://doi.org/10.4171/owr/2019/23\">https://doi.org/10.4171/owr/2019/23</a>","ama":"Anderson L, Hausel T, Mazzeo R, Schaposnik L. Geometry and physics of Higgs bundles. <i>Oberwolfach Reports</i>. 2020;16(2):1357-1417. doi:<a href=\"https://doi.org/10.4171/owr/2019/23\">10.4171/owr/2019/23</a>","mla":"Anderson, Lara, et al. “Geometry and Physics of Higgs Bundles.” <i>Oberwolfach Reports</i>, vol. 16, no. 2, EMS Press, 2020, pp. 1357–417, doi:<a href=\"https://doi.org/10.4171/owr/2019/23\">10.4171/owr/2019/23</a>.","ieee":"L. Anderson, T. Hausel, R. Mazzeo, and L. Schaposnik, “Geometry and physics of Higgs bundles,” <i>Oberwolfach Reports</i>, vol. 16, no. 2. EMS Press, pp. 1357–1417, 2020."},"department":[{"_id":"TaHa"}],"day":"04","month":"06","status":"public","date_published":"2020-06-04T00:00:00Z","article_processing_charge":"No","oa_version":"None","issue":"2","page":"1357-1417","intvolume":"        16","title":"Geometry and physics of Higgs bundles","publication_identifier":{"issn":["1660-8933"]}},{"date_updated":"2026-07-06T13:57:35Z","publisher":"Societe Mathematique de France","language":[{"iso":"eng"}],"publication":"Annales Scientifiques de l'Ecole Normale Superieure","arxiv":1,"quality_controlled":"1","isi":1,"publication_status":"published","abstract":[{"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":"eng"},{"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. ","lang":"fre"}],"year":"2020","main_file_link":[{"url":"https://arxiv.org/abs/1708.08013","open_access":"1"}],"article_type":"original","_id":"8539","doi":"10.24033/asens.2431","date_created":"2020-09-20T22:01:38Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","das_tickbox":"1","department":[{"_id":"TaHa"}],"citation":{"ama":"Su C, Zhao G, Zhong C. On the K-theory stable bases of the springer resolution. <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. 2020;53(3):663-671. doi:<a href=\"https://doi.org/10.24033/asens.2431\">10.24033/asens.2431</a>","ieee":"C. Su, G. Zhao, and C. Zhong, “On the K-theory stable bases of the springer resolution,” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>, vol. 53, no. 3. Societe Mathematique de France, pp. 663–671, 2020.","mla":"Su, C., et al. “On the K-Theory Stable Bases of the Springer Resolution.” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>, vol. 53, no. 3, Societe Mathematique de France, 2020, pp. 663–71, doi:<a href=\"https://doi.org/10.24033/asens.2431\">10.24033/asens.2431</a>.","short":"C. Su, G. Zhao, C. Zhong, Annales Scientifiques de l’Ecole Normale Superieure 53 (2020) 663–671.","chicago":"Su, C., Gufang Zhao, and C. Zhong. “On the K-Theory Stable Bases of the Springer Resolution.” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. Societe Mathematique de France, 2020. <a href=\"https://doi.org/10.24033/asens.2431\">https://doi.org/10.24033/asens.2431</a>.","apa":"Su, C., Zhao, G., &#38; Zhong, C. (2020). On the K-theory stable bases of the springer resolution. <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. Societe Mathematique de France. <a href=\"https://doi.org/10.24033/asens.2431\">https://doi.org/10.24033/asens.2431</a>","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."},"author":[{"full_name":"Su, C.","last_name":"Su","first_name":"C."},{"last_name":"Zhao","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","first_name":"Gufang","full_name":"Zhao, Gufang","orcid":"0000-0001-7361-2882"},{"first_name":"C.","last_name":"Zhong","full_name":"Zhong, C."}],"type":"journal_article","volume":53,"oa_version":"Preprint","article_processing_charge":"No","date_published":"2020-06-01T00:00:00Z","status":"public","month":"06","day":"01","scopus_import":"1","issue":"3","title":"On the K-theory stable bases of the springer resolution","publication_identifier":{"issn":["0012-9593"]},"intvolume":"        53","page":"663-671","external_id":{"arxiv":["1708.08013"],"isi":["000592182600004"]}},{"isi":1,"publication_status":"published","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. "}],"arxiv":1,"quality_controlled":"1","ddc":["500","570"],"publisher":"National Academy of Sciences","language":[{"iso":"eng"}],"publication":"Proceedings of the National Academy of Sciences of the United States of America","corr_author":"1","date_updated":"2026-06-18T18:17:35Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1073/pnas.1812015116","date_created":"2018-12-11T11:45:08Z","_id":"196","pmid":1,"year":"2019","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1073/pnas.1812015116"}],"article_type":"original","month":"02","related_material":{"link":[{"relation":"press_release","description":"News on IST Webpage","url":"https://ist.ac.at/en/news/famous-sandpile-model-shown-to-move-like-a-traveling-sand-dune/"}]},"day":"19","oa_version":"Published Version","article_processing_charge":"No","date_published":"2019-02-19T00:00:00Z","status":"public","volume":116,"department":[{"_id":"CaGu"},{"_id":"GaTk"},{"_id":"TaHa"}],"citation":{"apa":"Lang, M., &#38; Shkolnikov, M. (2019). Harmonic dynamics of the Abelian sandpile. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.1812015116\">https://doi.org/10.1073/pnas.1812015116</a>","ista":"Lang M, Shkolnikov M. 2019. Harmonic dynamics of the Abelian sandpile. Proceedings of the National Academy of Sciences of the United States of America. 116(8), 2821–2830.","short":"M. Lang, M. Shkolnikov, Proceedings of the National Academy of Sciences of the United States of America 116 (2019) 2821–2830.","chicago":"Lang, Moritz, and Mikhail Shkolnikov. “Harmonic Dynamics of the Abelian Sandpile.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences, 2019. <a href=\"https://doi.org/10.1073/pnas.1812015116\">https://doi.org/10.1073/pnas.1812015116</a>.","ieee":"M. Lang and M. Shkolnikov, “Harmonic dynamics of the Abelian sandpile,” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 116, no. 8. National Academy of Sciences, pp. 2821–2830, 2019.","mla":"Lang, Moritz, and Mikhail Shkolnikov. “Harmonic Dynamics of the Abelian Sandpile.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 116, no. 8, National Academy of Sciences, 2019, pp. 2821–30, doi:<a href=\"https://doi.org/10.1073/pnas.1812015116\">10.1073/pnas.1812015116</a>.","ama":"Lang M, Shkolnikov M. Harmonic dynamics of the Abelian sandpile. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. 2019;116(8):2821-2830. doi:<a href=\"https://doi.org/10.1073/pnas.1812015116\">10.1073/pnas.1812015116</a>"},"author":[{"last_name":"Lang","first_name":"Moritz","id":"29E0800A-F248-11E8-B48F-1D18A9856A87","full_name":"Lang, Moritz"},{"orcid":"0000-0002-4310-178X","full_name":"Shkolnikov, Mikhail","id":"35084A62-F248-11E8-B48F-1D18A9856A87","first_name":"Mikhail","last_name":"Shkolnikov"}],"type":"journal_article","page":"2821-2830","external_id":{"isi":["000459074400013"],"pmid":[" 30728300"],"arxiv":["1806.10823"]},"publication_identifier":{"eissn":["1091-6490"]},"title":"Harmonic dynamics of the Abelian sandpile","intvolume":"       116","issue":"8","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","scopus_import":"1"},{"date_published":"2019-09-15T00:00:00Z","status":"public","article_processing_charge":"No","oa_version":"Preprint","day":"15","month":"09","author":[{"full_name":"Kalinin, Nikita","first_name":"Nikita","last_name":"Kalinin"},{"last_name":"Shkolnikov","id":"35084A62-F248-11E8-B48F-1D18A9856A87","first_name":"Mikhail","full_name":"Shkolnikov, Mikhail","orcid":"0000-0002-4310-178X"}],"type":"journal_article","citation":{"short":"N. Kalinin, M. Shkolnikov, European Journal of Mathematics 5 (2019) 909–928.","chicago":"Kalinin, Nikita, and Mikhail Shkolnikov. “Tropical Formulae for Summation over a Part of SL(2,Z).” <i>European Journal of Mathematics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s40879-018-0218-0\">https://doi.org/10.1007/s40879-018-0218-0</a>.","apa":"Kalinin, N., &#38; Shkolnikov, M. (2019). Tropical formulae for summation over a part of SL(2,Z). <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-018-0218-0\">https://doi.org/10.1007/s40879-018-0218-0</a>","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.","ama":"Kalinin N, Shkolnikov M. Tropical formulae for summation over a part of SL(2,Z). <i>European Journal of Mathematics</i>. 2019;5(3):909–928. doi:<a href=\"https://doi.org/10.1007/s40879-018-0218-0\">10.1007/s40879-018-0218-0</a>","ieee":"N. Kalinin and M. Shkolnikov, “Tropical formulae for summation over a part of SL(2,Z),” <i>European Journal of Mathematics</i>, vol. 5, no. 3. Springer Nature, pp. 909–928, 2019.","mla":"Kalinin, Nikita, and Mikhail Shkolnikov. “Tropical Formulae for Summation over a Part of SL(2,Z).” <i>European Journal of Mathematics</i>, vol. 5, no. 3, Springer Nature, 2019, pp. 909–928, doi:<a href=\"https://doi.org/10.1007/s40879-018-0218-0\">10.1007/s40879-018-0218-0</a>."},"department":[{"_id":"TaHa"}],"volume":5,"intvolume":"         5","title":"Tropical formulae for summation over a part of SL(2,Z)","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"external_id":{"arxiv":["1711.02089"]},"project":[{"grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"page":"909–928","scopus_import":1,"publist_id":"7382","issue":"3","quality_controlled":"1","arxiv":1,"publication_status":"published","date_updated":"2021-01-12T07:56:46Z","publication":"European Journal of Mathematics","language":[{"iso":"eng"}],"publisher":"Springer Nature","date_created":"2018-12-11T11:46:29Z","doi":"10.1007/s40879-018-0218-0","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","oa":1,"article_type":"original","main_file_link":[{"url":"https://arxiv.org/abs/1711.02089","open_access":"1"}],"year":"2019","ec_funded":1,"_id":"441"},{"title":"The wonderful compactification for quantum groups","intvolume":"        99","page":"778-806","external_id":{"isi":["000470025900008"]},"scopus_import":"1","license":"https://creativecommons.org/licenses/by/4.0/","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"issue":"3","publist_id":"8052","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","status":"public","date_published":"2019-06-01T00:00:00Z","month":"06","day":"01","department":[{"_id":"TaHa"}],"citation":{"mla":"Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” <i>Journal of the London Mathematical Society</i>, vol. 99, no. 3, Wiley, 2019, pp. 778–806, doi:<a href=\"https://doi.org/10.1112/jlms.12193\">10.1112/jlms.12193</a>.","ieee":"I. V. Ganev, “The wonderful compactification for quantum groups,” <i>Journal of the London Mathematical Society</i>, vol. 99, no. 3. Wiley, pp. 778–806, 2019.","ama":"Ganev IV. The wonderful compactification for quantum groups. <i>Journal of the London Mathematical Society</i>. 2019;99(3):778-806. doi:<a href=\"https://doi.org/10.1112/jlms.12193\">10.1112/jlms.12193</a>","ista":"Ganev IV. 2019. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. 99(3), 778–806.","apa":"Ganev, I. V. (2019). The wonderful compactification for quantum groups. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.12193\">https://doi.org/10.1112/jlms.12193</a>","short":"I.V. Ganev, Journal of the London Mathematical Society 99 (2019) 778–806.","chicago":"Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” <i>Journal of the London Mathematical Society</i>. Wiley, 2019. <a href=\"https://doi.org/10.1112/jlms.12193\">https://doi.org/10.1112/jlms.12193</a>."},"author":[{"last_name":"Ganev","first_name":"Iordan V","id":"447491B8-F248-11E8-B48F-1D18A9856A87","full_name":"Ganev, Iordan V"}],"type":"journal_article","volume":99,"doi":"10.1112/jlms.12193","date_created":"2018-12-11T11:44:06Z","has_accepted_license":"1","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","year":"2019","_id":"5","ddc":["510"],"quality_controlled":"1","file_date_updated":"2020-07-14T12:46:35Z","isi":1,"publication_status":"published","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."}],"date_updated":"2023-09-19T10:13:08Z","file":[{"date_updated":"2020-07-14T12:46:35Z","access_level":"open_access","file_name":"2019_Wiley_Ganev.pdf","checksum":"1be56239b2cd740a0e9a084f773c22f6","date_created":"2020-01-07T13:31:53Z","file_size":431754,"creator":"kschuh","file_id":"7238","content_type":"application/pdf","relation":"main_file"}],"publisher":"Wiley","language":[{"iso":"eng"}],"publication":"Journal of the London Mathematical Society"},{"intvolume":"         2","title":"How to Sheafify an Elliptic Quantum Group","publication_identifier":{"issn":["2523-3041"],"eissn":["2523-305X"],"eisbn":["9783030041618"],"isbn":["9783030041601"]},"external_id":{"arxiv":["1803.06627"]},"OA_place":"repository","page":"675-691","acknowledgement":"Y.Y. would like to thank the organizers of the MATRIX program Geometric R-Matrices: from Geometry to Probability for their kind invitation, and many participants of the program for useful discussions, including Vassily Gorbounov, Andrei Okounkov, Allen Knutson, Hitoshi Konno, Paul Zinn-Justin. Proposition 1 and Sect. 3.3 are new, for which we thank Hitoshi Konno for interesting discussions and communications. These notes were written when both authors were visiting the Perimeter Institute for Theoretical Physics (PI). We are grateful to PI for the hospitality.","article_processing_charge":"No","status":"public","date_published":"2019-03-25T00:00:00Z","oa_version":"Preprint","month":"03","day":"25","author":[{"id":"360D8648-F248-11E8-B48F-1D18A9856A87","first_name":"Yaping","last_name":"Yang","full_name":"Yang, Yaping"},{"full_name":"Zhao, Gufang","last_name":"Zhao","first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87"}],"type":"book_chapter","department":[{"_id":"TaHa"}],"citation":{"ista":"Yang Y, Zhao G. 2019.How to Sheafify an Elliptic Quantum Group. In: 2017 MATRIX Annals. MATRIX Book Series, vol. 2, 675–691.","apa":"Yang, Y., &#38; Zhao, G. (2019). How to Sheafify an Elliptic Quantum Group. In <i>2017 MATRIX Annals</i> (Vol. 2, pp. 675–691). Cham: Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-04161-8_54\">https://doi.org/10.1007/978-3-030-04161-8_54</a>","chicago":"Yang, Yaping, and Gufang Zhao. “How to Sheafify an Elliptic Quantum Group.” In <i>2017 MATRIX Annals</i>, 2:675–91. MXBS. Cham: Springer International Publishing, 2019. <a href=\"https://doi.org/10.1007/978-3-030-04161-8_54\">https://doi.org/10.1007/978-3-030-04161-8_54</a>.","short":"Y. Yang, G. Zhao, in:, 2017 MATRIX Annals, Springer International Publishing, Cham, 2019, pp. 675–691.","mla":"Yang, Yaping, and Gufang Zhao. “How to Sheafify an Elliptic Quantum Group.” <i>2017 MATRIX Annals</i>, vol. 2, Springer International Publishing, 2019, pp. 675–91, doi:<a href=\"https://doi.org/10.1007/978-3-030-04161-8_54\">10.1007/978-3-030-04161-8_54</a>.","ieee":"Y. Yang and G. Zhao, “How to Sheafify an Elliptic Quantum Group,” in <i>2017 MATRIX Annals</i>, vol. 2, Cham: Springer International Publishing, 2019, pp. 675–691.","ama":"Yang Y, Zhao G. How to Sheafify an Elliptic Quantum Group. In: <i>2017 MATRIX Annals</i>. Vol 2. MXBS. Cham: Springer International Publishing; 2019:675-691. doi:<a href=\"https://doi.org/10.1007/978-3-030-04161-8_54\">10.1007/978-3-030-04161-8_54</a>"},"series_title":"MXBS","volume":2,"alternative_title":["MATRIX Book Series"],"date_created":"2025-07-10T13:31:38Z","doi":"10.1007/978-3-030-04161-8_54","OA_type":"green","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1803.06627","open_access":"1"}],"year":"2019","_id":"19987","quality_controlled":"1","arxiv":1,"abstract":[{"text":"These lecture notes are based on Yang’s talk at the MATRIX program Geometric R-Matrices: from Geometry to Probability, at the University of Melbourne, Dec. 18–22, 2017, and Zhao’s talk at Perimeter Institute for Theoretical Physics in January 2018. We give an introductory survey of the results in Yang and Zhao (Quiver varieties and elliptic quantum groups, 2017. arxiv1708.01418). We discuss a sheafified elliptic quantum group associated to any symmetric Kac-Moody Lie algebra. The sheafification is obtained by applying the equivariant elliptic cohomological theory to the moduli space of representations of a preprojective algebra. By construction, the elliptic quantum group naturally acts on the equivariant elliptic cohomology of Nakajima quiver varieties. As an application, we obtain a relation between the sheafified elliptic quantum group and the global affine Grassmannian over an elliptic curve.","lang":"eng"}],"publication_status":"published","date_updated":"2025-09-23T11:59:52Z","place":"Cham","publication":"2017 MATRIX Annals","publisher":"Springer International Publishing","language":[{"iso":"eng"}]},{"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.25537/dm.2019v24.1135-1177","has_accepted_license":"1","date_created":"2020-02-02T23:01:06Z","_id":"7436","year":"2019","article_type":"original","file_date_updated":"2020-07-14T12:47:58Z","isi":1,"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. "}],"publication_status":"published","arxiv":1,"ddc":["510"],"quality_controlled":"1","publisher":"EMS Press","language":[{"iso":"eng"}],"publication":"Documenta Mathematica","date_updated":"2023-10-17T07:42:21Z","file":[{"creator":"dernst","date_created":"2020-02-03T06:26:12Z","file_size":469730,"relation":"main_file","content_type":"application/pdf","file_id":"7438","checksum":"9a1a64bd49ab03fa4f738fb250fc4f90","file_name":"2019_DocumMath_Srivastava.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:58Z"}],"page":"1135-1177","external_id":{"arxiv":["1809.08970"],"isi":["000517806400019"]},"title":"On derived equivalences of k3 surfaces in positive characteristic","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"intvolume":"        24","scopus_import":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"05","day":"20","oa_version":"Published Version","article_processing_charge":"No","date_published":"2019-05-20T00:00:00Z","status":"public","volume":24,"department":[{"_id":"TaHa"}],"citation":{"ama":"Srivastava TK. On derived equivalences of k3 surfaces in positive characteristic. <i>Documenta Mathematica</i>. 2019;24:1135-1177. doi:<a href=\"https://doi.org/10.25537/dm.2019v24.1135-1177\">10.25537/dm.2019v24.1135-1177</a>","mla":"Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.” <i>Documenta Mathematica</i>, vol. 24, EMS Press, 2019, pp. 1135–77, doi:<a href=\"https://doi.org/10.25537/dm.2019v24.1135-1177\">10.25537/dm.2019v24.1135-1177</a>.","ieee":"T. K. Srivastava, “On derived equivalences of k3 surfaces in positive characteristic,” <i>Documenta Mathematica</i>, vol. 24. EMS Press, pp. 1135–1177, 2019.","short":"T.K. Srivastava, Documenta Mathematica 24 (2019) 1135–1177.","chicago":"Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.” <i>Documenta Mathematica</i>. EMS Press, 2019. <a href=\"https://doi.org/10.25537/dm.2019v24.1135-1177\">https://doi.org/10.25537/dm.2019v24.1135-1177</a>.","ista":"Srivastava TK. 2019. On derived equivalences of k3 surfaces in positive characteristic. Documenta Mathematica. 24, 1135–1177.","apa":"Srivastava, T. K. (2019). On derived equivalences of k3 surfaces in positive characteristic. <i>Documenta Mathematica</i>. EMS Press. <a href=\"https://doi.org/10.25537/dm.2019v24.1135-1177\">https://doi.org/10.25537/dm.2019v24.1135-1177</a>"},"type":"journal_article","author":[{"id":"4D046628-F248-11E8-B48F-1D18A9856A87","first_name":"Tanya K","last_name":"Srivastava","full_name":"Srivastava, Tanya K"}]},{"author":[{"full_name":"Hausel, Tamas","orcid":"0000-0002-9582-2634","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamas"},{"id":"43D735EE-F248-11E8-B48F-1D18A9856A87","first_name":"Martin","last_name":"Mereb","full_name":"Mereb, Martin"},{"full_name":"Wong, Michael","first_name":"Michael","last_name":"Wong"}],"type":"journal_article","citation":{"ieee":"T. Hausel, M. Mereb, and M. Wong, “Arithmetic and representation theory of wild character varieties,” <i>Journal of the European Mathematical Society</i>, vol. 21, no. 10. EMS Press, pp. 2995–3052, 2019.","mla":"Hausel, Tamás, et al. “Arithmetic and Representation Theory of Wild Character Varieties.” <i>Journal of the European Mathematical Society</i>, vol. 21, no. 10, EMS Press, 2019, pp. 2995–3052, doi:<a href=\"https://doi.org/10.4171/JEMS/896\">10.4171/JEMS/896</a>.","ama":"Hausel T, Mereb M, Wong M. Arithmetic and representation theory of wild character varieties. <i>Journal of the European Mathematical Society</i>. 2019;21(10):2995-3052. doi:<a href=\"https://doi.org/10.4171/JEMS/896\">10.4171/JEMS/896</a>","apa":"Hausel, T., Mereb, M., &#38; Wong, M. (2019). Arithmetic and representation theory of wild character varieties. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/JEMS/896\">https://doi.org/10.4171/JEMS/896</a>","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.","chicago":"Hausel, Tamás, Martin Mereb, and Michael Wong. “Arithmetic and Representation Theory of Wild Character Varieties.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2019. <a href=\"https://doi.org/10.4171/JEMS/896\">https://doi.org/10.4171/JEMS/896</a>.","short":"T. Hausel, M. Mereb, M. Wong, Journal of the European Mathematical Society 21 (2019) 2995–3052."},"department":[{"_id":"TaHa"}],"volume":21,"date_published":"2019-10-01T00:00:00Z","status":"public","article_processing_charge":"No","oa_version":"Preprint","day":"01","month":"10","scopus_import":"1","publist_id":"7384","issue":"10","intvolume":"        21","title":"Arithmetic and representation theory of wild character varieties","publication_identifier":{"eissn":["1435-9855"]},"external_id":{"isi":["000480413600002"],"arxiv":["1604.03382"]},"project":[{"call_identifier":"FP7","grant_number":"320593","_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces"}],"page":"2995-3052","date_updated":"2026-07-06T11:54:39Z","publication":"Journal of the European Mathematical Society","language":[{"iso":"eng"}],"publisher":"EMS Press","quality_controlled":"1","arxiv":1,"publication_status":"published","abstract":[{"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.","lang":"eng"}],"isi":1,"article_type":"original","main_file_link":[{"url":"https://arxiv.org/abs/1604.03382","open_access":"1"}],"year":"2019","ec_funded":1,"_id":"439","date_created":"2018-12-11T11:46:29Z","doi":"10.4171/JEMS/896","das_tickbox":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1},{"date_updated":"2026-07-06T12:24:07Z","publication":"Proceedings of the American Mathematical Society","publisher":"American Mathematical Society","language":[{"iso":"eng"}],"quality_controlled":"1","arxiv":1,"isi":1,"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. "}],"publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1810.07039","open_access":"1"}],"article_type":"original","year":"2019","_id":"6986","ec_funded":1,"date_created":"2019-11-04T16:10:50Z","doi":"10.1090/proc/14586","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","das_tickbox":"1","oa":1,"type":"journal_article","author":[{"id":"42A24CCC-F248-11E8-B48F-1D18A9856A87","first_name":"Penghui","last_name":"Li","full_name":"Li, Penghui"}],"department":[{"_id":"TaHa"}],"citation":{"ama":"Li P. A colimit of traces of reflection groups. <i>Proceedings of the American Mathematical Society</i>. 2019;147(11):4597-4604. doi:<a href=\"https://doi.org/10.1090/proc/14586\">10.1090/proc/14586</a>","mla":"Li, Penghui. “A Colimit of Traces of Reflection Groups.” <i>Proceedings of the American Mathematical Society</i>, vol. 147, no. 11, American Mathematical Society, 2019, pp. 4597–604, doi:<a href=\"https://doi.org/10.1090/proc/14586\">10.1090/proc/14586</a>.","ieee":"P. Li, “A colimit of traces of reflection groups,” <i>Proceedings of the American Mathematical Society</i>, vol. 147, no. 11. American Mathematical Society, pp. 4597–4604, 2019.","chicago":"Li, Penghui. “A Colimit of Traces of Reflection Groups.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2019. <a href=\"https://doi.org/10.1090/proc/14586\">https://doi.org/10.1090/proc/14586</a>.","short":"P. Li, Proceedings of the American Mathematical Society 147 (2019) 4597–4604.","ista":"Li P. 2019. A colimit of traces of reflection groups. Proceedings of the American Mathematical Society. 147(11), 4597–4604.","apa":"Li, P. (2019). A colimit of traces of reflection groups. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/14586\">https://doi.org/10.1090/proc/14586</a>"},"volume":147,"article_processing_charge":"No","status":"public","date_published":"2019-11-01T00:00:00Z","oa_version":"Preprint","month":"11","day":"01","scopus_import":"1","issue":"11","intvolume":"       147","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"title":"A colimit of traces of reflection groups","project":[{"grant_number":"320593","call_identifier":"FP7","name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":["1810.07039"],"isi":["000488621700004"]},"page":"4597-4604"},{"date_created":"2018-12-11T11:45:43Z","doi":"10.3934/dcds.2018120","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1706.03062","open_access":"1"}],"year":"2018","_id":"303","quality_controlled":"1","arxiv":1,"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."}],"publication_status":"published","isi":1,"date_updated":"2023-09-12T07:45:37Z","publication":"Discrete and Continuous Dynamical Systems- Series A","language":[{"iso":"eng"}],"publisher":"AIMS","intvolume":"        38","title":"Introduction to tropical series and wave dynamic on them","external_id":{"arxiv":["1706.03062"],"isi":["000438818400007"]},"page":"2827 - 2849","scopus_import":"1","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.","publist_id":"7576","issue":"6","date_published":"2018-06-01T00:00:00Z","status":"public","article_processing_charge":"No","oa_version":"Submitted Version","day":"01","month":"06","type":"journal_article","author":[{"first_name":"Nikita","last_name":"Kalinin","full_name":"Kalinin, Nikita"},{"last_name":"Shkolnikov","first_name":"Mikhail","id":"35084A62-F248-11E8-B48F-1D18A9856A87","full_name":"Shkolnikov, Mikhail","orcid":"0000-0002-4310-178X"}],"citation":{"mla":"Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and Wave Dynamic on Them.” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 38, no. 6, AIMS, 2018, pp. 2827–49, doi:<a href=\"https://doi.org/10.3934/dcds.2018120\">10.3934/dcds.2018120</a>.","ieee":"N. Kalinin and M. Shkolnikov, “Introduction to tropical series and wave dynamic on them,” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 38, no. 6. AIMS, pp. 2827–2849, 2018.","ama":"Kalinin N, Shkolnikov M. Introduction to tropical series and wave dynamic on them. <i>Discrete and Continuous Dynamical Systems- Series A</i>. 2018;38(6):2827-2849. doi:<a href=\"https://doi.org/10.3934/dcds.2018120\">10.3934/dcds.2018120</a>","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.","apa":"Kalinin, N., &#38; Shkolnikov, M. (2018). Introduction to tropical series and wave dynamic on them. <i>Discrete and Continuous Dynamical Systems- Series A</i>. AIMS. <a href=\"https://doi.org/10.3934/dcds.2018120\">https://doi.org/10.3934/dcds.2018120</a>","short":"N. Kalinin, M. Shkolnikov, Discrete and Continuous Dynamical Systems- Series A 38 (2018) 2827–2849.","chicago":"Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and Wave Dynamic on Them.” <i>Discrete and Continuous Dynamical Systems- Series A</i>. AIMS, 2018. <a href=\"https://doi.org/10.3934/dcds.2018120\">https://doi.org/10.3934/dcds.2018120</a>."},"department":[{"_id":"TaHa"}],"volume":38},{"date_created":"2019-02-14T13:14:22Z","doi":"10.1112/plms.12111","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1407.7994","open_access":"1"}],"year":"2018","_id":"5999","quality_controlled":"1","arxiv":1,"isi":1,"publication_status":"published","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. "}],"date_updated":"2023-09-19T14:37:19Z","publication":"Proceedings of the London Mathematical Society","publisher":"Oxford University Press","language":[{"iso":"eng"}],"intvolume":"       116","publication_identifier":{"issn":["0024-6115"]},"title":"The cohomological Hall algebra of a preprojective algebra","external_id":{"arxiv":["1407.7994"],"isi":["000431506400001"]},"page":"1029-1074","scopus_import":"1","issue":"5","article_processing_charge":"No","status":"public","date_published":"2018-05-01T00:00:00Z","oa_version":"Preprint","month":"05","day":"01","author":[{"full_name":"Yang, Yaping","first_name":"Yaping","last_name":"Yang"},{"full_name":"Zhao, Gufang","first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","last_name":"Zhao"}],"type":"journal_article","department":[{"_id":"TaHa"}],"citation":{"ieee":"Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,” <i>Proceedings of the London Mathematical Society</i>, vol. 116, no. 5. Oxford University Press, pp. 1029–1074, 2018.","mla":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” <i>Proceedings of the London Mathematical Society</i>, vol. 116, no. 5, Oxford University Press, 2018, pp. 1029–74, doi:<a href=\"https://doi.org/10.1112/plms.12111\">10.1112/plms.12111</a>.","ama":"Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra. <i>Proceedings of the London Mathematical Society</i>. 2018;116(5):1029-1074. doi:<a href=\"https://doi.org/10.1112/plms.12111\">10.1112/plms.12111</a>","apa":"Yang, Y., &#38; Zhao, G. (2018). The cohomological Hall algebra of a preprojective algebra. <i>Proceedings of the London Mathematical Society</i>. Oxford University Press. <a href=\"https://doi.org/10.1112/plms.12111\">https://doi.org/10.1112/plms.12111</a>","ista":"Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 116(5), 1029–1074.","short":"Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018) 1029–1074.","chicago":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” <i>Proceedings of the London Mathematical Society</i>. Oxford University Press, 2018. <a href=\"https://doi.org/10.1112/plms.12111\">https://doi.org/10.1112/plms.12111</a>."},"volume":116},{"language":[{"iso":"eng"}],"publisher":"Springer","publication":"Contemporary Computational Mathematics","citation":{"mla":"Bondarenko, Andriy, et al. “There Is No Strongly Regular Graph with Parameters (460; 153; 32; 60).” <i>Contemporary Computational Mathematics</i>, Springer, 2018, pp. 131–34, doi:<a href=\"https://doi.org/10.1007/978-3-319-72456-0_7\">10.1007/978-3-319-72456-0_7</a>.","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 <i>Contemporary Computational Mathematics</i>, Springer, 2018, pp. 131–134.","ama":"Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. There is no strongly regular graph with parameters (460; 153; 32; 60). In: <i>Contemporary Computational Mathematics</i>. Springer; 2018:131-134. doi:<a href=\"https://doi.org/10.1007/978-3-319-72456-0_7\">10.1007/978-3-319-72456-0_7</a>","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.","apa":"Bondarenko, A., Mellit, A., Prymak, A., Radchenko, D., &#38; Viazovska, M. (2018). There is no strongly regular graph with parameters (460; 153; 32; 60). In <i>Contemporary Computational Mathematics</i> (pp. 131–134). Springer. <a href=\"https://doi.org/10.1007/978-3-319-72456-0_7\">https://doi.org/10.1007/978-3-319-72456-0_7</a>","short":"A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, M. Viazovska, in:, Contemporary Computational Mathematics, Springer, 2018, pp. 131–134.","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 <i>Contemporary Computational Mathematics</i>, 131–34. Springer, 2018. <a href=\"https://doi.org/10.1007/978-3-319-72456-0_7\">https://doi.org/10.1007/978-3-319-72456-0_7</a>."},"department":[{"_id":"TaHa"}],"date_updated":"2021-01-12T08:06:06Z","type":"book_chapter","author":[{"last_name":"Bondarenko","first_name":"Andriy","full_name":"Bondarenko, Andriy"},{"first_name":"Anton","id":"388D3134-F248-11E8-B48F-1D18A9856A87","last_name":"Mellit","full_name":"Mellit, Anton"},{"full_name":"Prymak, Andriy","first_name":"Andriy","last_name":"Prymak"},{"last_name":"Radchenko","first_name":"Danylo","full_name":"Radchenko, Danylo"},{"full_name":"Viazovska, Maryna","first_name":"Maryna","last_name":"Viazovska"}],"publication_status":"published","day":"23","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. "}],"month":"05","oa_version":"Preprint","arxiv":1,"date_published":"2018-05-23T00:00:00Z","quality_controlled":"1","status":"public","article_processing_charge":"No","_id":"61","publist_id":"7993","year":"2018","main_file_link":[{"url":"https://arxiv.org/abs/1509.06286","open_access":"1"}],"oa":1,"page":"131 - 134","external_id":{"arxiv":["1509.06286"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","extern":"1","title":"There is no strongly regular graph with parameters (460; 153; 32; 60)","doi":"10.1007/978-3-319-72456-0_7","date_created":"2018-12-11T11:44:25Z"},{"publication":"Proceedings of the National Academy of Sciences of the United States of America","language":[{"iso":"eng"}],"publisher":"National Academy of Sciences","date_updated":"2025-06-03T11:21:16Z","publication_status":"published","abstract":[{"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.","lang":"eng"}],"isi":1,"quality_controlled":"1","arxiv":1,"ec_funded":1,"_id":"64","article_type":"original","main_file_link":[{"url":"https://arxiv.org/abs/1806.09153","open_access":"1"}],"year":"2018","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_created":"2018-12-11T11:44:26Z","doi":"10.1073/pnas.1805847115","volume":115,"author":[{"full_name":"Kalinin, Nikita","last_name":"Kalinin","first_name":"Nikita"},{"full_name":"Guzmán Sáenz, Aldo","last_name":"Guzmán Sáenz","first_name":"Aldo"},{"full_name":"Prieto, Y","last_name":"Prieto","first_name":"Y"},{"full_name":"Shkolnikov, Mikhail","orcid":"0000-0002-4310-178X","last_name":"Shkolnikov","first_name":"Mikhail","id":"35084A62-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kalinina, V","last_name":"Kalinina","first_name":"V"},{"last_name":"Lupercio","first_name":"Ernesto","full_name":"Lupercio, Ernesto"}],"type":"journal_article","citation":{"short":"N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, E. Lupercio, Proceedings of the National Academy of Sciences of the United States of America 115 (2018) E8135–E8142.","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.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences, 2018. <a href=\"https://doi.org/10.1073/pnas.1805847115\">https://doi.org/10.1073/pnas.1805847115</a>.","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. Proceedings of the National Academy of Sciences of the United States of America. 115(35), E8135–E8142.","apa":"Kalinin, N., Guzmán Sáenz, A., Prieto, Y., Shkolnikov, M., Kalinina, V., &#38; Lupercio, E. (2018). Self-organized criticality and pattern emergence through the lens of tropical geometry. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.1805847115\">https://doi.org/10.1073/pnas.1805847115</a>","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. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. 2018;115(35):E8135-E8142. doi:<a href=\"https://doi.org/10.1073/pnas.1805847115\">10.1073/pnas.1805847115</a>","mla":"Kalinin, Nikita, et al. “Self-Organized Criticality and Pattern Emergence through the Lens of Tropical Geometry.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 115, no. 35, National Academy of Sciences, 2018, pp. E8135–42, doi:<a href=\"https://doi.org/10.1073/pnas.1805847115\">10.1073/pnas.1805847115</a>.","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,” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 115, no. 35. National Academy of Sciences, pp. E8135–E8142, 2018."},"department":[{"_id":"TaHa"}],"day":"28","month":"08","date_published":"2018-08-28T00:00:00Z","status":"public","article_processing_charge":"No","oa_version":"Preprint","issue":"35","publist_id":"7990","scopus_import":"1","external_id":{"arxiv":["1806.09153"],"isi":["000442861600009"]},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734"}],"page":"E8135 - E8142","intvolume":"       115","publication_identifier":{"issn":["0027-8424"]},"title":"Self-organized criticality and pattern emergence through the lens of tropical geometry"},{"publication":"Geometry and Physics: Volume I","publisher":"Oxford University Press","language":[{"iso":"eng"}],"author":[{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás","last_name":"Hausel","orcid":"0000-0002-9582-2634","full_name":"Hausel, Tamás"},{"full_name":"Mellit, Anton","first_name":"Anton","id":"388D3134-F248-11E8-B48F-1D18A9856A87","last_name":"Mellit"},{"full_name":"Pei, Du","last_name":"Pei","first_name":"Du"}],"date_updated":"2026-04-16T10:30:22Z","type":"book_chapter","department":[{"_id":"TaHa"}],"citation":{"apa":"Hausel, T., Mellit, A., &#38; Pei, D. (2018). Mirror symmetry with branes by equivariant verlinde formulas. In <i>Geometry and Physics: Volume I</i> (pp. 189–218). Oxford University Press. <a href=\"https://doi.org/10.1093/oso/9780198802013.003.0009\">https://doi.org/10.1093/oso/9780198802013.003.0009</a>","ista":"Hausel T, Mellit A, Pei D. 2018.Mirror symmetry with branes by equivariant verlinde formulas. In: Geometry and Physics: Volume I. , 189–218.","chicago":"Hausel, Tamás, Anton Mellit, and Du Pei. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” In <i>Geometry and Physics: Volume I</i>, 189–218. Oxford University Press, 2018. <a href=\"https://doi.org/10.1093/oso/9780198802013.003.0009\">https://doi.org/10.1093/oso/9780198802013.003.0009</a>.","short":"T. Hausel, A. Mellit, D. Pei, in:, Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218.","ieee":"T. Hausel, A. Mellit, and D. Pei, “Mirror symmetry with branes by equivariant verlinde formulas,” in <i>Geometry and Physics: Volume I</i>, Oxford University Press, 2018, pp. 189–218.","mla":"Hausel, Tamás, et al. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” <i>Geometry and Physics: Volume I</i>, Oxford University Press, 2018, pp. 189–218, doi:<a href=\"https://doi.org/10.1093/oso/9780198802013.003.0009\">10.1093/oso/9780198802013.003.0009</a>.","ama":"Hausel T, Mellit A, Pei D. Mirror symmetry with branes by equivariant verlinde formulas. In: <i>Geometry and Physics: Volume I</i>. Oxford University Press; 2018:189-218. doi:<a href=\"https://doi.org/10.1093/oso/9780198802013.003.0009\">10.1093/oso/9780198802013.003.0009</a>"},"month":"01","publication_status":"published","abstract":[{"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.","lang":"eng"}],"day":"01","article_processing_charge":"No","status":"public","date_published":"2018-01-01T00:00:00Z","quality_controlled":"1","oa_version":"None","_id":"6525","scopus_import":"1","year":"2018","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","page":"189-218","date_created":"2019-06-06T12:42:01Z","doi":"10.1093/oso/9780198802013.003.0009","publication_identifier":{"eisbn":["9780191840500"],"isbn":["9780198802013"]},"title":"Mirror symmetry with branes by equivariant verlinde formulas"},{"_id":"322","ec_funded":1,"year":"2018","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1412.7211"}],"oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","doi":"10.1016/j.jalgebra.2018.03.015","date_created":"2018-12-11T11:45:49Z","publisher":"World Scientific Publishing","language":[{"iso":"eng"}],"publication":"Journal of Algebra","date_updated":"2025-04-14T09:12:46Z","corr_author":"1","isi":1,"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."}],"publication_status":"published","arxiv":1,"quality_controlled":"1","publist_id":"7543","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","scopus_import":"1","page":"92 - 128","project":[{"call_identifier":"FP7","grant_number":"320593","_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces"}],"external_id":{"isi":["000433270600005"],"arxiv":["1412.7211"]},"title":"Quantizations of multiplicative hypertoric varieties at a root of unity","intvolume":"       506","volume":506,"department":[{"_id":"TaHa"}],"citation":{"ieee":"I. V. Ganev, “Quantizations of multiplicative hypertoric varieties at a root of unity,” <i>Journal of Algebra</i>, vol. 506. World Scientific Publishing, pp. 92–128, 2018.","mla":"Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” <i>Journal of Algebra</i>, vol. 506, World Scientific Publishing, 2018, pp. 92–128, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">10.1016/j.jalgebra.2018.03.015</a>.","ama":"Ganev IV. Quantizations of multiplicative hypertoric varieties at a root of unity. <i>Journal of Algebra</i>. 2018;506:92-128. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">10.1016/j.jalgebra.2018.03.015</a>","apa":"Ganev, I. V. (2018). Quantizations of multiplicative hypertoric varieties at a root of unity. <i>Journal of Algebra</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">https://doi.org/10.1016/j.jalgebra.2018.03.015</a>","ista":"Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 506, 92–128.","chicago":"Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” <i>Journal of Algebra</i>. World Scientific Publishing, 2018. <a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">https://doi.org/10.1016/j.jalgebra.2018.03.015</a>.","short":"I.V. Ganev, Journal of Algebra 506 (2018) 92–128."},"type":"journal_article","author":[{"full_name":"Ganev, Iordan V","id":"447491B8-F248-11E8-B48F-1D18A9856A87","first_name":"Iordan V","last_name":"Ganev"}],"month":"07","day":"15","oa_version":"Preprint","article_processing_charge":"No","date_published":"2018-07-15T00:00:00Z","status":"public"},{"oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1093/qmath/haw053","date_created":"2018-12-11T11:47:55Z","_id":"687","ec_funded":1,"year":"2017","main_file_link":[{"url":"https://arxiv.org/abs/1311.7172","open_access":"1"}],"isi":1,"publication_status":"published","abstract":[{"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.","lang":"eng"}],"arxiv":1,"quality_controlled":"1","publisher":"Oxford University Press","language":[{"iso":"eng"}],"publication":"Quarterly Journal of Mathematics","corr_author":"1","date_updated":"2025-09-10T14:15:30Z","page":"635 - 703","project":[{"call_identifier":"FP7","grant_number":"320593","_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces"}],"external_id":{"arxiv":["1311.7172"],"isi":["000404545300015"]},"publication_identifier":{"issn":["0033-5606"]},"title":"The critical CoHA of a quiver with potential","intvolume":"        68","issue":"2","publist_id":"7022","scopus_import":"1","month":"06","day":"01","oa_version":"Submitted Version","article_processing_charge":"No","status":"public","date_published":"2017-06-01T00:00:00Z","volume":68,"department":[{"_id":"TaHa"}],"citation":{"apa":"Davison, B. (2017). The critical CoHA of a quiver with potential. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haw053\">https://doi.org/10.1093/qmath/haw053</a>","ista":"Davison B. 2017. The critical CoHA of a quiver with potential. Quarterly Journal of Mathematics. 68(2), 635–703.","chicago":"Davison, Ben. “The Critical CoHA of a Quiver with Potential.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2017. <a href=\"https://doi.org/10.1093/qmath/haw053\">https://doi.org/10.1093/qmath/haw053</a>.","short":"B. Davison, Quarterly Journal of Mathematics 68 (2017) 635–703.","ieee":"B. Davison, “The critical CoHA of a quiver with potential,” <i>Quarterly Journal of Mathematics</i>, vol. 68, no. 2. Oxford University Press, pp. 635–703, 2017.","mla":"Davison, Ben. “The Critical CoHA of a Quiver with Potential.” <i>Quarterly Journal of Mathematics</i>, vol. 68, no. 2, Oxford University Press, 2017, pp. 635–703, doi:<a href=\"https://doi.org/10.1093/qmath/haw053\">10.1093/qmath/haw053</a>.","ama":"Davison B. The critical CoHA of a quiver with potential. <i>Quarterly Journal of Mathematics</i>. 2017;68(2):635-703. doi:<a href=\"https://doi.org/10.1093/qmath/haw053\">10.1093/qmath/haw053</a>"},"type":"journal_article","author":[{"id":"4634AB1E-F248-11E8-B48F-1D18A9856A87","first_name":"Ben","last_name":"Davison","orcid":"0000-0002-8944-4390","full_name":"Davison, Ben"}]}]