---
OA_place: publisher
OA_type: hybrid
_id: '18970'
abstract:
- lang: eng
text: Given a smooth projective curve C, nonabelian Hodge theory gives a diffeomorphism
between two different moduli spaces associated to C. The first is the moduli space
of Higgs bundles on C of rank n, which is equipped with the structure of an algebraic
completely integrable Hamiltonian system. The second is the character variety
of representations of the fundamental group of C into GL(n). In 2012, de Cataldo,
Hausel, and Migliorini [1] proposed the P=W conjecture which identifies the perverse
filtration on the cohomology of the Higgs moduli space with the weight filtration
on the cohomology of the character variety. Recently, in 2022, two independent
proofs of the P=W Conjecture appeared, in work of Maulik &Shen [2] and Hausel,
Mellit, Minets &Schiffmann [6]. The aim of the Arbeitsgemeinschaft was to understand
the P=W Conjecture and these two recent proofs.
acknowledgement: "The MFO and the workshop organizers would like to thank the\r\nNational
Science Foundation for supporting the participation of junior researchers\r\nby
the grant DMS-2230648, “US Junior Oberwolfach Fellows”. Moreover, the\r\nMFO and
the workshop organizers would like to thank the Oberwolfach Foundation for supporting
the participation of junior researchers in the Arbeitsgemeinschaft."
article_processing_charge: No
article_type: original
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
- first_name: Davesh
full_name: Maulik, Davesh
last_name: Maulik
- first_name: Anton
full_name: Mellit, Anton
last_name: Mellit
- first_name: Olivier
full_name: Schiffmann, Olivier
last_name: Schiffmann
- first_name: Junliang
full_name: Shen, Junliang
last_name: Shen
citation:
ama: 'Hausel T, Maulik D, Mellit A, Schiffmann O, Shen J. Arbeitsgemeinschaft: Geometry
and representation theory around the P=W conjecture. Oberwolfach Reports.
2024;21(2):949-1004. doi:10.4171/owr/2024/16'
apa: 'Hausel, T., Maulik, D., Mellit, A., Schiffmann, O., & Shen, J. (2024).
Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture.
Oberwolfach Reports. EMS Press. https://doi.org/10.4171/owr/2024/16'
chicago: 'Hausel, Tamás, Davesh Maulik, Anton Mellit, Olivier Schiffmann, and Junliang
Shen. “Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W
Conjecture.” Oberwolfach Reports. EMS Press, 2024. https://doi.org/10.4171/owr/2024/16.'
ieee: 'T. Hausel, D. Maulik, A. Mellit, O. Schiffmann, and J. Shen, “Arbeitsgemeinschaft:
Geometry and representation theory around the P=W conjecture,” Oberwolfach
Reports, vol. 21, no. 2. EMS Press, pp. 949–1004, 2024.'
ista: 'Hausel T, Maulik D, Mellit A, Schiffmann O, Shen J. 2024. Arbeitsgemeinschaft:
Geometry and representation theory around the P=W conjecture. Oberwolfach Reports.
21(2), 949–1004.'
mla: 'Hausel, Tamás, et al. “Arbeitsgemeinschaft: Geometry and Representation Theory
around the P=W Conjecture.” Oberwolfach Reports, vol. 21, no. 2, EMS Press,
2024, pp. 949–1004, doi:10.4171/owr/2024/16.'
short: T. Hausel, D. Maulik, A. Mellit, O. Schiffmann, J. Shen, Oberwolfach Reports
21 (2024) 949–1004.
date_created: 2025-01-29T15:34:22Z
date_published: 2024-05-05T00:00:00Z
date_updated: 2025-01-29T15:39:55Z
day: '05'
ddc:
- '500'
department:
- _id: TaHa
doi: 10.4171/owr/2024/16
has_accepted_license: '1'
intvolume: ' 21'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-sa/4.0/
main_file_link:
- open_access: '1'
url: https://doi.org/10.4171/owr/2024/16
month: '05'
oa: 1
oa_version: Published Version
page: 949-1004
publication: Oberwolfach Reports
publication_identifier:
eissn:
- 1660-8941
issn:
- 1660-8933
publication_status: published
publisher: EMS Press
quality_controlled: '1'
status: public
title: 'Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture'
tmp:
image: /images/cc_by_sa.png
legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode
name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC
BY-SA 4.0)
short: CC BY-SA (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2024'
...
---
OA_place: repository
OA_type: green
_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
arxiv: 1
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
- 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: 2025-09-04T11:56:33Z
day: '27'
department:
- _id: TaHa
doi: 10.1007/s00029-023-00914-2
external_id:
arxiv:
- '1810.01818'
isi:
- '001150684300001'
intvolume: ' 30'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1810.01818
month: '01'
oa: 1
oa_version: Preprint
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: Locally free representations of quivers over commutative Frobenius algebras
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 30
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_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
arxiv: 1
author:
- first_name: Shiyu
full_name: Shen, Shiyu
id: 544cccd3-9005-11ec-87bc-94aef1c5b814
last_name: Shen
orcid: 0000-0002-4444-8718
citation:
ama: Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic.
International Mathematics Research Notices. 2024;2024(7):6176-6208. 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, vol. 2024, no. 7. Oxford University
Press, pp. 6176–6208, 2024.
ista: Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive
characteristic. International Mathematics Research Notices. 2024(7), 6176–6208.
mla: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive
Characteristic.” International Mathematics Research Notices, vol. 2024,
no. 7, Oxford University Press, 2024, pp. 6176–208, doi:10.1093/imrn/rnae005.
short: S. Shen, International Mathematics Research Notices 2024 (2024) 6176–6208.
corr_author: '1'
date_created: 2024-02-14T12:16:17Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2025-09-09T08:30:06Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1093/imrn/rnae005
ec_funded: 1
external_id:
arxiv:
- '1810.12491'
isi:
- '001157898100001'
file:
- access_level: open_access
checksum: e3cd31ebb2e79b5b1f34d1c4ac9f5b0f
content_type: application/pdf
creator: dernst
date_created: 2024-07-22T11:41:57Z
date_updated: 2024-07-22T11:41:57Z
file_id: '17308'
file_name: 2024_IMRN_Shen.pdf
file_size: 1488981
relation: main_file
success: 1
file_date_updated: 2024-07-22T11:41:57Z
has_accepted_license: '1'
intvolume: ' 2024'
isi: 1
issue: '7'
keyword:
- General Mathematics
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '04'
oa: 1
oa_version: Published Version
page: 6176-6208
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: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tamely ramified geometric Langlands correspondence 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: 2024
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15248'
abstract:
- lang: eng
text: Applying the technique of p-adic integration, we prove the topological mirror
symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic
Higgs bundles for the structure groups SLn and PGLn, building on previous work
of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the E-polynomial
of the smooth moduli space of parabolic GLn-Higgs bundles is independent of the
degree of the underlying vector bundles.
acknowledgement: Shiyu Shen has received funding from the European Union's Horizon
2020 research and innovation program under the Marie Skłodowska-Curie grant agreement
No. 101034413.
article_number: '109616'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Shiyu
full_name: Shen, Shiyu
id: 544cccd3-9005-11ec-87bc-94aef1c5b814
last_name: Shen
orcid: 0000-0002-4444-8718
citation:
ama: Shen S. Mirror symmetry for parabolic Higgs bundles via p-adic integration.
Advances in Mathematics. 2024;443(5). doi:10.1016/j.aim.2024.109616
apa: Shen, S. (2024). Mirror symmetry for parabolic Higgs bundles via p-adic integration.
Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2024.109616
chicago: Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.”
Advances in Mathematics. Elsevier, 2024. https://doi.org/10.1016/j.aim.2024.109616.
ieee: S. Shen, “Mirror symmetry for parabolic Higgs bundles via p-adic integration,”
Advances in Mathematics, vol. 443, no. 5. Elsevier, 2024.
ista: Shen S. 2024. Mirror symmetry for parabolic Higgs bundles via p-adic integration.
Advances in Mathematics. 443(5), 109616.
mla: Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.”
Advances in Mathematics, vol. 443, no. 5, 109616, Elsevier, 2024, doi:10.1016/j.aim.2024.109616.
short: S. Shen, Advances in Mathematics 443 (2024).
corr_author: '1'
date_created: 2024-03-31T22:01:11Z
date_published: 2024-05-01T00:00:00Z
date_updated: 2025-09-04T13:21:18Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1016/j.aim.2024.109616
ec_funded: 1
external_id:
arxiv:
- '2302.02817'
isi:
- '001216128200001'
file:
- access_level: open_access
checksum: 68f2f08136ccf547891a16a2c0621e97
content_type: application/pdf
creator: dernst
date_created: 2024-07-22T12:10:03Z
date_updated: 2024-07-22T12:10:03Z
file_id: '17315'
file_name: 2024_AdvancesMath_Shen.pdf
file_size: 702889
relation: main_file
success: 1
file_date_updated: 2024-07-22T12:10:03Z
has_accepted_license: '1'
intvolume: ' 443'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
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: 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: Mirror symmetry for parabolic Higgs bundles via p-adic integration
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 443
year: '2024'
...
---
_id: '15339'
abstract:
- lang: eng
text: We define even very stable Higgs bundles and study the Hitchin map restricted
to their upward flows. In the GLn case, we classify the type (1,…,1) examples,
and find that they are governed by a root system formed by the roots of even height.
We discuss how the spectrum of equivariant cohomology of real and quaternionic
Grassmannians, 4n-spheres and the real Cayley plane appear to describe the Hitchin
map on even cominuscule upward flows. The even upward flows in question are the
same as upward flows in Higgs bundle moduli spaces for quasi-split inner real
forms. The latter spaces have been pioneered by Oscar García-Prada and his collaborators.
acknowledgement: Most of the research for this paper was done when the first author
visited the second author's group at IST Austria as a summer intern in 2022. The
second author was supported by an FWF grant "Geometry of the top of the nilpotent
cone" number P35847.
article_number: '2441009'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Miguel
full_name: González, Miguel
last_name: González
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
citation:
ama: González M, Hausel T. Hitchin map on even very stable upward flows. International
Journal of Mathematics. 2024;35(09). doi:10.1142/S0129167X2441009X
apa: González, M., & Hausel, T. (2024). Hitchin map on even very stable upward
flows. International Journal of Mathematics. World Scientific Publishing.
https://doi.org/10.1142/S0129167X2441009X
chicago: González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward
Flows.” International Journal of Mathematics. World Scientific Publishing,
2024. https://doi.org/10.1142/S0129167X2441009X.
ieee: M. González and T. Hausel, “Hitchin map on even very stable upward flows,”
International Journal of Mathematics, vol. 35, no. 09. World Scientific
Publishing, 2024.
ista: González M, Hausel T. 2024. Hitchin map on even very stable upward flows.
International Journal of Mathematics. 35(09), 2441009.
mla: González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward
Flows.” International Journal of Mathematics, vol. 35, no. 09, 2441009,
World Scientific Publishing, 2024, doi:10.1142/S0129167X2441009X.
short: M. González, T. Hausel, International Journal of Mathematics 35 (2024).
date_created: 2024-04-21T22:00:54Z
date_published: 2024-04-04T00:00:00Z
date_updated: 2025-09-04T13:40:37Z
day: '04'
department:
- _id: TaHa
doi: 10.1142/S0129167X2441009X
external_id:
arxiv:
- '2303.01404'
isi:
- '001251179200003'
intvolume: ' 35'
isi: 1
issue: '09'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2303.01404
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: International Journal of Mathematics
publication_identifier:
eissn:
- 1793-6519
issn:
- 0129-167X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hitchin map on even very stable upward flows
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 35
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '17292'
abstract:
- lang: eng
text: The Gibbons-Hawking ansatz provides a large family of circle-invariant hyperkähler
4-manifolds, and thus Calabi-Yau 2-folds. In this setting, we prove versions of
the Thomas conjecture on existence of special Lagrangian representatives of Hamiltonian
isotopy classes of Lagrangians, and the Thomas-Yau conjecture on longtime existence
of the Lagrangian mean curvature ow. We also make observations concerning closed
geodesics, curve shortening flow and minimal surfaces.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jason D.
full_name: Lotay, Jason D.
last_name: Lotay
- first_name: Goncalo
full_name: Oliveira, Goncalo
id: 58abbde8-f455-11eb-a497-98c8fd71b905
last_name: Oliveira
citation:
ama: Lotay JD, Oliveira G. Special Lagrangians, Lagrangian mean curvature flow and
the Gibbons-Hawking ansatz. Journal of Differential Geometry. 2024;126(3):1121-1184.
doi:10.4310/jdg/1717348872
apa: Lotay, J. D., & Oliveira, G. (2024). Special Lagrangians, Lagrangian mean
curvature flow and the Gibbons-Hawking ansatz. Journal of Differential Geometry.
International Press. https://doi.org/10.4310/jdg/1717348872
chicago: Lotay, Jason D., and Goncalo Oliveira. “Special Lagrangians, Lagrangian
Mean Curvature Flow and the Gibbons-Hawking Ansatz.” Journal of Differential
Geometry. International Press, 2024. https://doi.org/10.4310/jdg/1717348872.
ieee: J. D. Lotay and G. Oliveira, “Special Lagrangians, Lagrangian mean curvature
flow and the Gibbons-Hawking ansatz,” Journal of Differential Geometry,
vol. 126, no. 3. International Press, pp. 1121–1184, 2024.
ista: Lotay JD, Oliveira G. 2024. Special Lagrangians, Lagrangian mean curvature
flow and the Gibbons-Hawking ansatz. Journal of Differential Geometry. 126(3),
1121–1184.
mla: Lotay, Jason D., and Goncalo Oliveira. “Special Lagrangians, Lagrangian Mean
Curvature Flow and the Gibbons-Hawking Ansatz.” Journal of Differential Geometry,
vol. 126, no. 3, International Press, 2024, pp. 1121–84, doi:10.4310/jdg/1717348872.
short: J.D. Lotay, G. Oliveira, Journal of Differential Geometry 126 (2024) 1121–1184.
corr_author: '1'
date_created: 2024-07-22T07:45:31Z
date_published: 2024-03-01T00:00:00Z
date_updated: 2025-09-08T08:27:51Z
day: '01'
department:
- _id: TaHa
doi: 10.4310/jdg/1717348872
external_id:
arxiv:
- '2002.10391'
isi:
- '001271790200007'
intvolume: ' 126'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2002.10391
month: '03'
oa: 1
oa_version: Preprint
page: 1121-1184
publication: Journal of Differential Geometry
publication_identifier:
issn:
- 0022-040X
publication_status: published
publisher: International Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking
ansatz
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 126
year: '2024'
...
---
_id: '17437'
abstract:
- lang: eng
text: We prove that the zero-fiber of the moment map of a totally negative quiver
has rational singularities. Our proof consists in generalizing dimension bounds
on jet spaces of this fiber, which were introduced by Budur. We also transfer
the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau
categories, based on recent work of Davison. This has interesting arithmetic applications
on quiver moment maps and moduli spaces of objects in 2-Calabi-Yau categories.
First, we generalize results of Wyss on the asymptotic behaviour of counts of
jets of quiver moment maps over finite fields. Moreover, we interpret the limit
of counts of jets on a given moduli space as its p-adic volume under a canonical
measure analogous to the measure built by Carocci, Orecchia and Wyss on certain
moduli spaces of coherent sheaves.
acknowledgement: "I would like to warmly thank Dimitri Wyss for his guidance and supervision
and Nero Budur for helpful discussions and answering all my questions on his previous
works. I would also like to thank Francesca Carocci, Ben Davison, Lucien Hennecart
and Olivier Schiffmann for helpful remarks and discussions during the writing of
this paper. Finally, I would like to thank the anonymous referees for their careful
reading and suggesting improvements in the exposition.\r\nOpen access funding provided
by Institute of Science and Technology (IST Austria). This work was supported by
the Swiss National Science Foundation [No. 196960]. This project has also 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: Yes (via OA deal)
article_type: original
author:
- first_name: Tanguy
full_name: Vernet, Tanguy
id: 19f1e3bf-c59a-11ee-a1af-ed269948817b
last_name: Vernet
citation:
ama: Vernet T. Rational singularities for moment maps of totally negative quivers.
Transformation Groups. 2024. doi:10.1007/s00031-024-09873-0
apa: Vernet, T. (2024). Rational singularities for moment maps of totally negative
quivers. Transformation Groups. Springer Nature. https://doi.org/10.1007/s00031-024-09873-0
chicago: Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative
Quivers.” Transformation Groups. Springer Nature, 2024. https://doi.org/10.1007/s00031-024-09873-0.
ieee: T. Vernet, “Rational singularities for moment maps of totally negative quivers,”
Transformation Groups. Springer Nature, 2024.
ista: Vernet T. 2024. Rational singularities for moment maps of totally negative
quivers. Transformation Groups.
mla: Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative
Quivers.” Transformation Groups, Springer Nature, 2024, doi:10.1007/s00031-024-09873-0.
short: T. Vernet, Transformation Groups (2024).
corr_author: '1'
date_created: 2024-08-18T22:01:04Z
date_published: 2024-09-09T00:00:00Z
date_updated: 2025-09-08T08:56:08Z
day: '09'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00031-024-09873-0
ec_funded: 1
external_id:
isi:
- '001287455300001'
has_accepted_license: '1'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00031-024-09873-0
month: '09'
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: Transformation Groups
publication_identifier:
eissn:
- 1531-586X
issn:
- 1083-4362
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rational singularities for moment maps of totally negative quivers
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...
---
OA_place: publisher
OA_type: free access
_id: '18443'
abstract:
- lang: eng
text: "In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry
relation between\r\nthe hyperkähler structures on certain Higgs bundle moduli
spaces. As a consequence, they\r\nconjecture an equivalence between categories
of BBB and BAA-branes. At the classical\r\nlevel, this mirror symmetry is given
by T-duality between semi-flat hyperkähler structures on\r\nalgebraic integrable
systems.\r\nIn this thesis, we investigate the T-duality relation between hyperkähler
structures and the\r\ncorresponding branes on affine torus bundles. We use the
techniques of generalized geometry\r\nto show that semi-flat hyperkähler structures
are T-dual on algebraic integrable systems.\r\nWe also describe T-duality for
generalized branes. Motivated by Fourier-Mukai transform\r\nwe upgrade the T-duality
between generalized branes to T-duality of submanifolds endowed\r\nwith U(1)-bundles
and connections. This T-duality in the appropriate context specializes to\r\nT-duality
between BBB and BAA-branes.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Maria A
full_name: Sisak, Maria A
id: 44A03D04-AEA4-11E9-B225-EA2DE6697425
last_name: Sisak
citation:
ama: Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:10.15479/at:ista:18443
apa: Sisak, M. A. (2024). T-dual branes on hyperkähler manifolds. Institute
of Science and Technology Austria. https://doi.org/10.15479/at:ista:18443
chicago: Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of
Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18443.
ieee: M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science
and Technology Austria, 2024.
ista: Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science
and Technology Austria.
mla: Sisak, Maria A. T-Dual Branes on Hyperkähler Manifolds. Institute of
Science and Technology Austria, 2024, doi:10.15479/at:ista:18443.
short: M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science
and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-10-19T12:00:37Z
date_published: 2024-10-24T00:00:00Z
date_updated: 2026-04-07T12:42:44Z
day: '24'
ddc:
- '516'
degree_awarded: PhD
department:
- _id: GradSch
- _id: TaHa
doi: 10.15479/at:ista:18443
file:
- access_level: open_access
checksum: 8c4893e726aaa4b3efb82758da9b6851
content_type: application/pdf
creator: msisak
date_created: 2024-10-23T14:42:45Z
date_updated: 2024-10-23T14:42:45Z
file_id: '18467'
file_name: MASisak_dissertation.pdf
file_size: 1672547
relation: main_file
success: 1
- access_level: closed
checksum: 1831b072e861a1e5481024ca9d02b036
content_type: application/x-zip-compressed
creator: msisak
date_created: 2024-10-23T14:43:56Z
date_updated: 2024-10-24T08:09:13Z
file_id: '18468'
file_name: MASisak_source.zip
file_size: 617913
relation: source_file
file_date_updated: 2024-10-24T08:09:13Z
has_accepted_license: '1'
keyword:
- hyperkaehler geometry
- branes
- mirror symmetry
- T-duality
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: '178'
project:
- _id: 6286e8c4-2b32-11ec-9570-f5297902f67f
grant_number: '26069'
name: Branes on hyperkähler manifolds
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
title: T-dual branes on hyperkähler manifolds
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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: publisher
_id: '17156'
abstract:
- lang: eng
text: "This dissertation is the summary of the author’s work, concerning the relations
between\r\ncohomology rings of algebraic varieties and rings of functions on zero
schemes and fixed\r\npoint schemes. For most of the thesis, the focus is on smooth
complex varieties with\r\nan action of a principally paired group, e.g. a parabolic
subgroup of a reductive group.\r\nThe fundamental theorem 5.2.11 from co-authored
article [66] says that if the principal\r\nnilpotent has a unique zero, then the
zero scheme over the Kostant section is isomorphic\r\nto the spectrum of the equivariant
cohomology ring, remembering the grading in terms of\r\na C^* action. A similar
statement is proved also for the G-invariant functions on the total\r\nzero scheme
over the whole Lie algebra. Additionally, we are able to prove an analogous\r\nresult
for the GKM spaces, which poses the question on a joint generalisation.\r\nWe
also tackle the situation of a singular variety. As long as it is embedded in
a smooth\r\nvariety with regular action, we are able to study its cohomology as
well by means of\r\nthe zero scheme. In case of e.g. Schubert varieties this determines
the cohomology ring\r\ncompletely. In largest generality, this allows us to see
a significant part of the cohomology\r\nring.\r\nWe also show (Theorem 6.2.1)
that the cohomology ring of spherical varieties appears as\r\nthe ring of functions
on the zero scheme. The computational aspect is not easy, but one\r\ncan hope
that this can bring some concrete information about such cohomology rings.\r\nLastly,
the K-theory conjecture 6.3.1 is studied, with some results attained for GKM\r\nspaces.\r\nThe
thesis includes also an introduction to group actions on algebraic varieties.
In\r\nparticular, the vector fields associated to the actions are extensively
studied. We also\r\nprovide a version of the Kostant section for arbitrary principally
paired group, which\r\nparametrises the regular orbits in the Lie algebra of an
algebraic group. Before proving\r\nthe main theorem, we also include a historical
overview of the field. In particular we bring\r\ntogether the results of Akyildiz,
Carrell and Lieberman on non-equivariant cohomology\r\nrings."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Kamil P
full_name: Rychlewicz, Kamil P
id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425
last_name: Rychlewicz
citation:
ama: Rychlewicz KP. Equivariant cohomology and rings of functions. 2024. doi:10.15479/at:ista:17156
apa: Rychlewicz, K. P. (2024). Equivariant cohomology and rings of functions.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17156
chicago: Rychlewicz, Kamil P. “Equivariant Cohomology and Rings of Functions.” Institute
of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17156.
ieee: K. P. Rychlewicz, “Equivariant cohomology and rings of functions,” Institute
of Science and Technology Austria, 2024.
ista: Rychlewicz KP. 2024. Equivariant cohomology and rings of functions. Institute
of Science and Technology Austria.
mla: Rychlewicz, Kamil P. Equivariant Cohomology and Rings of Functions.
Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17156.
short: K.P. Rychlewicz, Equivariant Cohomology and Rings of Functions, Institute
of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-06-23T15:07:06Z
date_published: 2024-06-25T00:00:00Z
date_updated: 2026-04-07T12:55:46Z
day: '25'
ddc:
- '516'
degree_awarded: PhD
department:
- _id: TaHa
- _id: GradSch
doi: 10.15479/at:ista:17156
file:
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file_size: 2761814
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checksum: 7bbadb1fbc9ed2a1ecf54597f88af99c
content_type: application/pdf
creator: krychlew
date_created: 2024-06-26T20:58:24Z
date_updated: 2024-06-26T20:58:24Z
file_id: '17180'
file_name: thesis.pdf
file_size: 3695952
relation: main_file
file_date_updated: 2024-06-26T21:00:14Z
has_accepted_license: '1'
keyword:
- equivariant cohomology
- zero schemes
- algebraic groups
- Lie algebras
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: '117'
project:
- _id: 34cd0f74-11ca-11ed-8bc3-bf0492a14a24
grant_number: '26525'
name: Topology of open smooth varieties with a torus action
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '17157'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
title: Equivariant cohomology and rings of functions
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
_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
arxiv: 1
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
orcid: 0000-0001-6889-1418
- 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).
corr_author: '1'
date_created: 2023-08-06T22:01:10Z
date_published: 2023-07-15T00:00:00Z
date_updated: 2025-09-09T12:45:32Z
day: '15'
department:
- _id: MiLe
- _id: TaHa
doi: 10.1103/PhysRevB.108.045115
ec_funded: 1
external_id:
arxiv:
- '2203.12666'
isi:
- '001532067800001'
intvolume: ' 108'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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
arxiv: 1
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).
corr_author: '1'
date_created: 2023-08-27T22:01:16Z
date_published: 2023-08-03T00:00:00Z
date_updated: 2025-04-14T07:54:52Z
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: '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
arxiv: 1
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
- 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.
corr_author: '1'
date_created: 2023-08-27T22:01:18Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2025-04-14T09:12:46Z
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: '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).
corr_author: '1'
date_created: 2023-01-22T23:00:55Z
date_published: 2023-01-10T00:00:00Z
date_updated: 2024-10-09T21:03:29Z
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: '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
arxiv: 1
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.
corr_author: '1'
date_created: 2023-07-23T22:01:14Z
date_published: 2023-06-21T00:00:00Z
date_updated: 2025-04-14T07:54:52Z
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: '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
arxiv: 1
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: 2025-04-14T09:12:46Z
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: '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
arxiv: 1
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.
corr_author: '1'
date_created: 2023-04-02T22:01:11Z
date_published: 2022-08-29T00:00:00Z
date_updated: 2025-04-14T07:44:01Z
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'
...
---
OA_place: publisher
OA_type: gold
_id: '19984'
abstract:
- lang: eng
text: "The first part of this paper is a survey of mathematical results on mirror
symmetry phenomena between Hitchin systems for Langlands dual groups. The second
part introduces\r\nand discusses multiplicity algebras of the Hitchin system on
Lagrangians, and considers\r\ncorresponding conjectural structures on their mirror."
acknowledgement: "The author thanks Nigel Hitchin for introducing him to Higgs bundles
during 1995–1998,\r\nsuggesting the SYZ picture for Langlands dual Hitchin systems
in 1996, and for the\r\nmore recent collaborations [29, 30]. He also thanks David
Ben-Zvi, Pierre-Henri Chaudouard, Pierre Deligne, Ron Donagi, Sergei Gukov, Jochen
Heinloth, Vadim Kaloshin,\r\nJoel Kamnitzer, Gérard Laumon, Anton Mellit, David
Nadler, Andy Neitzke, Ngô Bao\r\nChâu, Michael Thaddeus, Tony Pantev, Du Pei, Richárd
Rimányi, Leonid Rybnikov, Vivek\r\nShende, Balázs Szendrői, András Szenes, Fernando
Rodriguez-Villegas, Edward Witten,\r\nand Zhiwei Yun for discussions about the subjects
in this paper over the years. Thanks are\r\nalso due to Hülya Argüz, Jakub Löwit,
Balázs Szendrői, and Nigel Hitchin for the careful\r\nreading of the paper."
article_processing_charge: No
arxiv: 1
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
citation:
ama: 'Hausel T. Enhanced mirror symmetry for Langlands dual Hitchin systems. In:
International Congress of Mathematicians. EMS Press; 2022:2228-2249. doi:10.4171/icm2022/164'
apa: 'Hausel, T. (2022). Enhanced mirror symmetry for Langlands dual Hitchin systems.
In International Congress of Mathematicians (pp. 2228–2249). virtuel: EMS
Press. https://doi.org/10.4171/icm2022/164'
chicago: Hausel, Tamás. “Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems.”
In International Congress of Mathematicians, 2228–49. EMS Press, 2022.
https://doi.org/10.4171/icm2022/164.
ieee: T. Hausel, “Enhanced mirror symmetry for Langlands dual Hitchin systems,”
in International Congress of Mathematicians, EMS Press, 2022, pp. 2228–2249.
ista: 'Hausel T. 2022.Enhanced mirror symmetry for Langlands dual Hitchin systems.
In: International Congress of Mathematicians. , 2228–2249.'
mla: Hausel, Tamás. “Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems.”
International Congress of Mathematicians, EMS Press, 2022, pp. 2228–49,
doi:10.4171/icm2022/164.
short: T. Hausel, in:, International Congress of Mathematicians, EMS Press, 2022,
pp. 2228–2249.
conference:
end_date: 2022-07-14
location: virtuel
name: 'ICM: International Congress of Mathematicians'
start_date: 2022-07-06
corr_author: '1'
date_created: 2025-07-10T13:13:36Z
date_published: 2022-07-15T00:00:00Z
date_updated: 2025-09-24T09:12:13Z
day: '15'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.4171/icm2022/164
external_id:
arxiv:
- '2112.09455'
file:
- access_level: open_access
checksum: d2b9d4cf51c854f1082d8dc18c5853b1
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creator: dernst
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file_name: 2022_ICM_Hausel.pdf
file_size: 655370
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oa_version: Published Version
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publication: International Congress of Mathematicians
publication_identifier:
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isbn:
- '9783985470587'
publication_status: published
publisher: EMS Press
quality_controlled: '1'
status: public
title: Enhanced mirror symmetry for Langlands dual Hitchin systems
tmp:
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short: CC BY (4.0)
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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
arxiv: 1
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
- 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.
corr_author: '1'
date_created: 2022-01-30T23:01:34Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2025-04-15T06:53:08Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00222-021-01093-7
external_id:
arxiv:
- '2101.08583'
isi:
- '000745495400001'
file:
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checksum: a382ba75acebc9adfb8fe56247cb410e
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file_size: 1069538
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success: 1
file_date_updated: 2023-02-27T07:30:47Z
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language:
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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)
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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
arxiv: 1
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.
corr_author: '1'
date_created: 2022-02-20T23:01:33Z
date_published: 2022-02-05T00:00:00Z
date_updated: 2024-10-09T21:01:37Z
day: '05'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/jlms.12515
external_id:
arxiv:
- '1712.10260'
isi:
- '000751600600001'
file:
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checksum: 8bd0fd9694be894a191857ddf27678f0
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relation: main_file
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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
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(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: '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
arxiv: 1
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.
corr_author: '1'
date_created: 2021-08-31T12:51:40Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2025-04-14T07:43:49Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/jlms.12506
ec_funded: 1
external_id:
arxiv:
- '1811.05376'
isi:
- '000755205700001'
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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
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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'
...