---
_id: '21489'
abstract:
- lang: eng
text: We study Kirillov algebras attached to minuscule highest weight representations
of semisimple Lie algebras. They can be viewed as equivariant cohomology algebras
of partial flag varieties. Real structures on the varieties then induce involutions
of these algebras. We describe how these involutions act on the spectra of minuscule
Kirillov algebras, and model the fixed points via the equivariant cohomology of
real partial flag varieties. We then use this model to characterise freeness of
the fixed point coordinate ring over the appropriate base. As an application,
we recover a q = -1 phenomenon of Stembridge in the minuscule case by geometric
means.
acknowledgement: 'I would like to thank Tamás Hausel for introducing me to this area
of mathematics and for his constant guidance. I would also like to thank Jakub Löwit
and Miguel González for fruitful discussions and many helpful comments on this paper.
This work was done during the author’s PhD studies at the Institute of Science and
Technology Austria (ISTA). It was funded by the Austrian Science Fund (FWF) 10.55776/P35847.
Open access funding provided by Institute of Science and Technology (IST Austria). '
article_processing_charge: Yes (via OA deal)
arxiv: 1
author:
- first_name: Mischa M
full_name: Elkner, Mischa M
id: 477faa59-080d-11ed-979a-c693ab7638ab
last_name: Elkner
citation:
ama: Elkner MM. On involutions of minuscule Kirillov algebras induced by real structures.
Transformation Groups. 2026. doi:10.1007/s00031-026-09958-y
apa: Elkner, M. M. (2026). On involutions of minuscule Kirillov algebras induced
by real structures. Transformation Groups. Springer Nature. https://doi.org/10.1007/s00031-026-09958-y
chicago: Elkner, Mischa M. “On Involutions of Minuscule Kirillov Algebras Induced
by Real Structures.” Transformation Groups. Springer Nature, 2026. https://doi.org/10.1007/s00031-026-09958-y.
ieee: M. M. Elkner, “On involutions of minuscule Kirillov algebras induced by real
structures,” Transformation Groups. Springer Nature, 2026.
ista: Elkner MM. 2026. On involutions of minuscule Kirillov algebras induced by
real structures. Transformation Groups.
mla: Elkner, Mischa M. “On Involutions of Minuscule Kirillov Algebras Induced by
Real Structures.” Transformation Groups, Springer Nature, 2026, doi:10.1007/s00031-026-09958-y.
short: M.M. Elkner, Transformation Groups (2026).
corr_author: '1'
date_created: 2026-03-23T15:10:43Z
date_published: 2026-03-14T00:00:00Z
date_updated: 2026-03-24T08:26:10Z
day: '14'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00031-026-09958-y
external_id:
arxiv:
- '2411.16270'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00031-026-09958-y
month: '03'
oa: 1
oa_version: None
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: Transformation Groups
publication_identifier:
eissn:
- 1531-586X
issn:
- 1083-4362
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On involutions of minuscule Kirillov algebras induced by real structures
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
year: '2026'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: diamond
_id: '21718'
abstract:
- lang: eng
text: "In this paper, we consider the big algebra recently introduced by Hausel
for the GLn-action on the coordinate ring of the matrix space Mat(n,r). In particular,
we obtain explicit formulas for the big algebra generators in terms of differential
operators with polynomial coefficients. We show that big algebras in type A are
commutative and relate them to the Bethe subalgebra in the Yangian Y(gln). We
apply these results to big algebras of symmetric powers of the standard representation
of GLn.\r\n."
acknowledgement: "I would like to express my gratitude to Tam´as Hausel for introducing
me to the subject and\r\nfor his constant guidance throughout this work. I would
also like to thank Tam´as Hausel,\r\nMischa Elkner, Jakub L¨owit, Anton Mellit,
Marino Romero, Leonid Rybnikov for many fruitful\r\ndiscussions and feedback on
earlier drafts of this paper. We are grateful to the anonymous\r\nreferees for many
useful comments and suggestions that improved the manuscript. This work was done
during the author’s PhD studies at the Institute of Science and Technology Austria
(ISTA). The author was supported by the Austrian Science Fund (FWF) grant\r\n“Geometry
of the tip of the global nilpotent cone” no. 10.55776/P35847 and the DOC Fellowship
of the Austrian Academy of Sciences. The author also acknowledges the long-term
program\r\nof support of the Ukrainian research teams at the Polish Academy of Sciences
carried out in\r\ncollaboration with the U.S. National Academy of Sciences with
the financial support of external\r\npartners. For open access purposes, the author
has applied a CC BY public copyright license\r\nto any author-accepted manuscript
version arising from this submission."
article_number: '024'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nhok T
full_name: Ngo, Nhok T
id: 28e53c8c-896a-11ed-bdf8-f809043ce2f0
last_name: Ngo
citation:
ama: 'Ngo NT. Big algebra in type A for the coordinate ring of the matrix space.
Symmetry, Integrability and Geometry: Methods and Applications. 2026;22.
doi:10.3842/SIGMA.2026.024'
apa: 'Ngo, N. T. (2026). Big algebra in type A for the coordinate ring of the matrix
space. Symmetry, Integrability and Geometry: Methods and Applications.
National Academy of Science of Ukraine. https://doi.org/10.3842/SIGMA.2026.024'
chicago: 'Ngo, Nhok T. “Big Algebra in Type A for the Coordinate Ring of the Matrix
Space.” Symmetry, Integrability and Geometry: Methods and Applications.
National Academy of Science of Ukraine, 2026. https://doi.org/10.3842/SIGMA.2026.024.'
ieee: 'N. T. Ngo, “Big algebra in type A for the coordinate ring of the matrix space,”
Symmetry, Integrability and Geometry: Methods and Applications, vol. 22.
National Academy of Science of Ukraine, 2026.'
ista: 'Ngo NT. 2026. Big algebra in type A for the coordinate ring of the matrix
space. Symmetry, Integrability and Geometry: Methods and Applications. 22, 024.'
mla: 'Ngo, Nhok T. “Big Algebra in Type A for the Coordinate Ring of the Matrix
Space.” Symmetry, Integrability and Geometry: Methods and Applications,
vol. 22, 024, National Academy of Science of Ukraine, 2026, doi:10.3842/SIGMA.2026.024.'
short: 'N.T. Ngo, Symmetry, Integrability and Geometry: Methods and Applications
22 (2026).'
corr_author: '1'
date_created: 2026-04-12T22:01:51Z
date_published: 2026-03-14T00:00:00Z
date_updated: 2026-04-16T06:11:12Z
day: '14'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.3842/SIGMA.2026.024
external_id:
arxiv:
- '2501.04605'
file:
- access_level: open_access
checksum: 29b28b5f8717ed1a084a2b551d0fd284
content_type: application/pdf
creator: dernst
date_created: 2026-04-16T06:06:54Z
date_updated: 2026-04-16T06:06:54Z
file_id: '21740'
file_name: 2026_SIGMA_Ngo.pdf
file_size: 975460
relation: main_file
success: 1
file_date_updated: 2026-04-16T06:06:54Z
has_accepted_license: '1'
intvolume: ' 22'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
- _id: e6c64f42-ab3c-11f0-94c7-a95658059ccc
grant_number: '27483'
name: Big algebras in classical types
publication: 'Symmetry, Integrability and Geometry: Methods and Applications'
publication_identifier:
eissn:
- 1815-0659
publication_status: published
publisher: National Academy of Science of Ukraine
quality_controlled: '1'
scopus_import: '1'
status: public
title: Big algebra in type A for the coordinate ring of the matrix space
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: 22
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21751'
abstract:
- lang: eng
text: 'We define a certain class of simple varieties over a field k by a constructive
recipe and show how to control their (equivariant) truncating invariants. Consequently,
we prove that on simple varieties: (i) if k = k and char k = p, the p-adic cyclotomic
trace is an equivalence; (ii) if k = Q, the Goodwillie–Jones trace is an isomorphism
in degree zero; (iii) we can control homotopy invariant K-theory KH, which is
equivariantly formal and determined by its topological counterparts. Simple varieties
are quite special, but encompass important singular examples appearing in geometric
representation theory. We, in particular, show that both finite and affine Schubert
varieties for GLn lie in this class, so all the above results hold for them. '
acknowledgement: "This work was supported by a DOC Fellowship of the Austrian Academy
of Sciences at the Institute of Science and Technology Austria (ISTA) and by an
Erasmus+ staff mobility training. It took place during the author’s visit to Laboratoire
de Mathématiques d’Orsay in the course of his PhD at the Institute of Science and
Technology Austria. First and foremost, I would like to thank Matthew Morrow for
discussions, explanations and ideas without which this work would not have been
carried out. I would further like to thank Brian Conrad for providing an amazing
reference on projective cones in appropriate generality, to Vova Sosnilo for carefully
discussing – among other things – the derived nilinvariance for quotients by any
linearly reductive group, and to Adeel Khan, Timo Richarz, Matthias Wendt and Xinwen
Zhu for helpful conversations\r\nabout the results. I would moreover like to thank
the referee for the very useful comments."
article_number: rnag058
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jakub
full_name: Löwit, Jakub
id: e3b80ae2-eb8e-11eb-b029-9aef4a9108a0
last_name: Löwit
citation:
ama: Löwit J. Equivariant localizing invariants of simple varieties. International
Mathematics Research Notices. 2026;2026(7). doi:10.1093/imrn/rnag058
apa: Löwit, J. (2026). Equivariant localizing invariants of simple varieties. International
Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnag058
chicago: Löwit, Jakub. “Equivariant Localizing Invariants of Simple Varieties.”
International Mathematics Research Notices. Oxford University Press, 2026.
https://doi.org/10.1093/imrn/rnag058.
ieee: J. Löwit, “Equivariant localizing invariants of simple varieties,” International
Mathematics Research Notices, vol. 2026, no. 7. Oxford University Press, 2026.
ista: Löwit J. 2026. Equivariant localizing invariants of simple varieties. International
Mathematics Research Notices. 2026(7), rnag058.
mla: Löwit, Jakub. “Equivariant Localizing Invariants of Simple Varieties.” International
Mathematics Research Notices, vol. 2026, no. 7, rnag058, Oxford University
Press, 2026, doi:10.1093/imrn/rnag058.
short: J. Löwit, International Mathematics Research Notices 2026 (2026).
corr_author: '1'
date_created: 2026-04-19T22:07:48Z
date_published: 2026-04-01T00:00:00Z
date_updated: 2026-05-06T06:36:25Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1093/imrn/rnag058
external_id:
arxiv:
- '2507.09392'
file:
- access_level: open_access
checksum: 306f4567b7b2dcf38e23f7b55a27514e
content_type: application/pdf
creator: dernst
date_created: 2026-05-06T06:35:05Z
date_updated: 2026-05-06T06:35:05Z
file_id: '21803'
file_name: 2026_IMRN_Loewit.pdf
file_size: 1663246
relation: main_file
success: 1
file_date_updated: 2026-05-06T06:35:05Z
has_accepted_license: '1'
intvolume: ' 2026'
issue: '7'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: 901e2a43-16d5-11f0-9cad-9cead34748d6
grant_number: '27004'
name: Arithmetic, geometry, topology and representation theory arising from the
affine Grassmannian
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: Equivariant localizing invariants of simple varieties
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: 2026
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '21931'
abstract:
- lang: eng
text: In 1873, James C. Maxwell conjectured that the electric field generated by
n point charges in generic position has at most (n-1)^2 isolated zeroes. The first
(nonoptimal) upper bound was only obtained in 2007 by Gabrielov, Novikov, and
Shapiro, who also posed two additional interesting conjectures. In this article,
we give the best upper bound known to date on the number of zeroes of the electric
field, and construct a counterexample to Conjecture 1.8 by Gabrielov, Novikov,
and Shapiro that the number of equilibria cannot exceed those of the distance
function defined by the unit point charges. Finally, we note that it is quite
possible that Maxwell's quadratic upper bound is not tight, so it is prudent to
find lower bounds. Hence, we also explore examples and construct configurations
of charges achieving the highest ratios of the number of electric field zeroes
by point charges found to this day.
article_number: e70163
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Goncalo
full_name: Oliveira, Goncalo
id: 58abbde8-f455-11eb-a497-98c8fd71b905
last_name: Oliveira
citation:
ama: Edelsbrunner H, Fillmore CD, Oliveira G. Counting equilibria of the electrostatic
potential. Proceedings of the London Mathematical Society. 2026;132(5).
doi:10.1112/plms.70163
apa: Edelsbrunner, H., Fillmore, C. D., & Oliveira, G. (2026). Counting equilibria
of the electrostatic potential. Proceedings of the London Mathematical Society.
Wiley. https://doi.org/10.1112/plms.70163
chicago: Edelsbrunner, Herbert, Christopher D Fillmore, and Goncalo Oliveira. “Counting
Equilibria of the Electrostatic Potential.” Proceedings of the London Mathematical
Society. Wiley, 2026. https://doi.org/10.1112/plms.70163.
ieee: H. Edelsbrunner, C. D. Fillmore, and G. Oliveira, “Counting equilibria of
the electrostatic potential,” Proceedings of the London Mathematical Society,
vol. 132, no. 5. Wiley, 2026.
ista: Edelsbrunner H, Fillmore CD, Oliveira G. 2026. Counting equilibria of the
electrostatic potential. Proceedings of the London Mathematical Society. 132(5),
e70163.
mla: Edelsbrunner, Herbert, et al. “Counting Equilibria of the Electrostatic Potential.”
Proceedings of the London Mathematical Society, vol. 132, no. 5, e70163,
Wiley, 2026, doi:10.1112/plms.70163.
short: H. Edelsbrunner, C.D. Fillmore, G. Oliveira, Proceedings of the London Mathematical
Society 132 (2026).
corr_author: '1'
date_created: 2026-05-31T22:02:13Z
date_published: 2026-05-01T00:00:00Z
date_updated: 2026-06-02T09:24:18Z
day: '01'
department:
- _id: HeEd
- _id: TaHa
doi: 10.1112/plms.70163
external_id:
arxiv:
- '2501.05315'
intvolume: ' 132'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2501.05315
month: '05'
oa: 1
oa_version: Preprint
publication: Proceedings of the London Mathematical Society
publication_identifier:
eissn:
- 1460-244X
issn:
- 0024-6115
publication_status: published
publisher: Wiley
quality_controlled: '1'
related_material:
record:
- id: '21050'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Counting equilibria of the electrostatic potential
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 132
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18154'
abstract:
- lang: eng
text: 'In 1976, Deligne and Lusztig realized the representation theory of finite
groups of Lie type inside étale cohomology of certain algebraic varieties. Recently,
a p-adic version of this theory started to emerge: there are p-adic Deligne–Lusztig
spaces, whose cohomology encodes representation theoretic information for p-adic
groups – for instance, it partially realizes the local Langlands correspondence
with characteristic zero coefficients. However, the parallel case of coefficients
of positive characteristic ℓ≠p has not been inspected so far. The purpose of
this article is to initiate such an inspection. In particular, we relate cohomology
of certain p-adic Deligne–Lusztig spaces to Vignéras''s modular local Langlands
correspondence for GLn.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jakub
full_name: Löwit, Jakub
id: e3b80ae2-eb8e-11eb-b029-9aef4a9108a0
last_name: Löwit
citation:
ama: Löwit J. On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn.
Journal of Algebra. 2025;663(2):81-118. doi:10.1016/j.jalgebra.2024.08.033
apa: Löwit, J. (2025). On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties
for GLn. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2024.08.033
chicago: Löwit, Jakub. “On modulo ℓ Cohomology of P-Adic Deligne–Lusztig Varieties
for GLn.” Journal of Algebra. Elsevier, 2025. https://doi.org/10.1016/j.jalgebra.2024.08.033.
ieee: J. Löwit, “On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for
GLn,” Journal of Algebra, vol. 663, no. 2. Elsevier, pp. 81–118, 2025.
ista: Löwit J. 2025. On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties
for GLn. Journal of Algebra. 663(2), 81–118.
mla: Löwit, Jakub. “On modulo ℓ Cohomology of P-Adic Deligne–Lusztig Varieties for
GLn.” Journal of Algebra, vol. 663, no. 2, Elsevier, 2025, pp. 81–118,
doi:10.1016/j.jalgebra.2024.08.033.
short: J. Löwit, Journal of Algebra 663 (2025) 81–118.
corr_author: '1'
date_created: 2024-09-29T22:01:37Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-02-27T12:32:40Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1016/j.jalgebra.2024.08.033
external_id:
arxiv:
- '2404.11176'
isi:
- '001325207800001'
file:
- access_level: open_access
checksum: eb240e93c178e48429ad918c9058f1fe
content_type: application/pdf
creator: dernst
date_created: 2025-01-13T08:57:57Z
date_updated: 2025-01-13T08:57:57Z
file_id: '18830'
file_name: 2024_JourAlgebra_Loewit.pdf
file_size: 731175
relation: main_file
success: 1
file_date_updated: 2025-01-13T08:57:57Z
has_accepted_license: '1'
intvolume: ' 663'
isi: 1
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 81-118
publication: Journal of Algebra
publication_identifier:
eissn:
- 1090-266X
issn:
- 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn
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: 663
year: '2025'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '20043'
abstract:
- lang: eng
text: We establish an isomorphism of complex K-theory of the moduli space M of
“SL n ”-Higgs bundles of degree d and rank n (in the sense of Hausel–Thaddeus)
and twisted complex K-theory of the orbifold M of PGL n -Higgs bundles of degree
e, where (n,d)=(n,e)=1. Along the way, we prove the vanishing of torsion for H
∗ ( M ) and certain twisted complex K-theory groups of M . We also extend Arinkin’s
autoduality of compactified Jacobian to a derived equivalence between SL n -
and PGL n -Hitchin systems over the elliptic locus. In the appendix, we develop
a formalism of G-sheaves of spectra, generalising equivariant homotopy theory
to a relative setting.
acknowledgement: "It is a pleasure to thank Tom Baird for sharing his insights about
vanishing of torsion for H.M{1\r\n2/. Furthermore, we would like to thank him for
bringing [25] to our attention. We also thank Alexander Kupers for enlightening
conversations about the Atiyah–Hirzebruch spectral sequence and for pointing out
a reference. We are grateful to Victoria Hoskins and Simon Pepin-Lehalleur for sharing
a preprint of their recent paper on a motivic version of topological mirror symmetry
and for useful remarks on Section 6. Anne Larsen pointed out that our previous proof
Lemma 4.5 was incomplete, we thank her for bringing this to our attention. We are
grateful to the anonymous referee for many valuable comments that have improved
the paper tremendously. The report we received was one of the most detailed referee
report either of us has ever seen. We thank them for their hard work and the resulting
contribution to this paper. Michael Groechenig was supported by an NSERC discovery
grant and an Alfred P. Sloan\r\nfellowship. Shiyu Shen has received funding from
the European Union’s Horizon 2020 research\r\nand innovation program under the Marie
Skłodowska-Curie grant agreement No. 101034413."
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Michael
full_name: Groechenig, Michael
last_name: Groechenig
- first_name: Shiyu
full_name: Shen, Shiyu
id: 544cccd3-9005-11ec-87bc-94aef1c5b814
last_name: Shen
orcid: 0000-0002-4444-8718
citation:
ama: Groechenig M, Shen S. Complex K-theory of moduli spaces of Higgs bundles. Journal
of the European Mathematical Society. 2025. doi:10.4171/jems/1601
apa: Groechenig, M., & Shen, S. (2025). Complex K-theory of moduli spaces of
Higgs bundles. Journal of the European Mathematical Society. EMS Press.
https://doi.org/10.4171/jems/1601
chicago: Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces
of Higgs Bundles.” Journal of the European Mathematical Society. EMS Press,
2025. https://doi.org/10.4171/jems/1601.
ieee: M. Groechenig and S. Shen, “Complex K-theory of moduli spaces of Higgs bundles,”
Journal of the European Mathematical Society. EMS Press, 2025.
ista: Groechenig M, Shen S. 2025. Complex K-theory of moduli spaces of Higgs bundles.
Journal of the European Mathematical Society.
mla: Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of
Higgs Bundles.” Journal of the European Mathematical Society, EMS Press,
2025, doi:10.4171/jems/1601.
short: M. Groechenig, S. Shen, Journal of the European Mathematical Society (2025).
corr_author: '1'
date_created: 2025-07-21T07:54:50Z
date_published: 2025-03-20T00:00:00Z
date_updated: 2026-02-19T09:24:54Z
day: '20'
department:
- _id: TaHa
doi: 10.4171/jems/1601
ec_funded: 1
external_id:
arxiv:
- '2212.10695'
isi:
- '001608254800001'
isi: 1
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.4171/JEMS/1601
month: '03'
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: Journal of the European Mathematical Society
publication_identifier:
eissn:
- 1435-9863
issn:
- 1435-9855
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
status: public
title: Complex K-theory of moduli spaces of Higgs bundles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '19071'
abstract:
- lang: eng
text: "An action of a complex reductive group G on a smooth projective variety X
is regular when all regular unipotent elements in G act with finitely many fixed
points. Then the complex G\r\n-equivariant cohomology ring of X is isomorphic
to the coordinate ring of a certain regular fixed point scheme. Examples include
partial flag varieties, smooth Schubert varieties and Bott-Samelson varieties.
We also show that a more general version of the fixed point scheme allows a generalisation
to GKM spaces, such as toric varieties."
acknowledgement: 'The first author was supported by an FWF grant “Geometry of the
top of the nilpotent cone” number P 35847. The second author was supported by an
Austrian Academy of Sciences DOC Fellowship “Topology of open smooth varieties with
a torus action”. '
article_number: '1'
article_processing_charge: Yes
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: Kamil P
full_name: Rychlewicz, Kamil P
id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425
last_name: Rychlewicz
citation:
ama: Hausel T, Rychlewicz KP. Spectrum of equivariant cohomology as a fixed point
scheme. Epijournal de Geometrie Algebrique. 2025;9. doi:10.46298/epiga.2025.12591
apa: Hausel, T., & Rychlewicz, K. P. (2025). Spectrum of equivariant cohomology
as a fixed point scheme. Epijournal de Geometrie Algebrique. EPI Sciences.
https://doi.org/10.46298/epiga.2025.12591
chicago: Hausel, Tamás, and Kamil P Rychlewicz. “Spectrum of Equivariant Cohomology
as a Fixed Point Scheme.” Epijournal de Geometrie Algebrique. EPI Sciences,
2025. https://doi.org/10.46298/epiga.2025.12591.
ieee: T. Hausel and K. P. Rychlewicz, “Spectrum of equivariant cohomology as a fixed
point scheme,” Epijournal de Geometrie Algebrique, vol. 9. EPI Sciences,
2025.
ista: Hausel T, Rychlewicz KP. 2025. Spectrum of equivariant cohomology as a fixed
point scheme. Epijournal de Geometrie Algebrique. 9, 1.
mla: Hausel, Tamás, and Kamil P. Rychlewicz. “Spectrum of Equivariant Cohomology
as a Fixed Point Scheme.” Epijournal de Geometrie Algebrique, vol. 9, 1,
EPI Sciences, 2025, doi:10.46298/epiga.2025.12591.
short: T. Hausel, K.P. Rychlewicz, Epijournal de Geometrie Algebrique 9 (2025).
corr_author: '1'
date_created: 2025-02-23T23:01:56Z
date_published: 2025-02-03T00:00:00Z
date_updated: 2025-04-15T06:31:58Z
day: '03'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.46298/epiga.2025.12591
external_id:
arxiv:
- '2212.11836'
file:
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checksum: 3915c6f117461502f7103878460428df
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date_created: 2025-02-25T06:53:27Z
date_updated: 2025-02-25T06:53:27Z
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month: '02'
oa: 1
oa_version: Published Version
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grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
- _id: 34cd0f74-11ca-11ed-8bc3-bf0492a14a24
grant_number: '26525'
name: Topology of open smooth varieties with a torus action
publication: Epijournal de Geometrie Algebrique
publication_identifier:
eissn:
- 2491-6765
publication_status: published
publisher: EPI Sciences
quality_controlled: '1'
related_material:
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scopus_import: '1'
status: public
title: Spectrum of equivariant cohomology as a fixed point scheme
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short: CC BY-SA (4.0)
type: journal_article
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...
---
OA_place: publisher
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_id: '19621'
abstract:
- lang: eng
text: In this paper we obtain a complete description of all indecomposable characters
(central positive-definite functions) of inductive limits of the symmetric groups
under block diagonal embedding. As a corollary we obtain the full classification
of the isomorphism classes of these inductive limits.
acknowledgement: The authors were partially supported by the “Long-term program of
support of the Ukrainian research teams at the Polish Academy of Sciences carried
out in collaboration with the U.S. National Academy of Sciences with the financial
support of external partners”. The second author was also supported by the Austrian
Science Fund (FWF) grant “Geometry of the tip of the global nilpotent cone” no.
10.55776/P35847
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Nikolay
full_name: Nessonov, Nikolay
last_name: Nessonov
- first_name: Nhok T
full_name: Ngo, Nhok T
id: 28e53c8c-896a-11ed-bdf8-f809043ce2f0
last_name: Ngo
citation:
ama: Nessonov N, Ngo NT. Indecomposable characters of inductive limits of symmetric
groups. Representation Theory. 2025;29(8):256-288. doi:10.1090/ert/689
apa: Nessonov, N., & Ngo, N. T. (2025). Indecomposable characters of inductive
limits of symmetric groups. Representation Theory. American Mathematical
Society. https://doi.org/10.1090/ert/689
chicago: Nessonov, Nikolay, and Nhok T Ngo. “Indecomposable Characters of Inductive
Limits of Symmetric Groups.” Representation Theory. American Mathematical
Society, 2025. https://doi.org/10.1090/ert/689.
ieee: N. Nessonov and N. T. Ngo, “Indecomposable characters of inductive limits
of symmetric groups,” Representation Theory, vol. 29, no. 8. American Mathematical
Society, pp. 256–288, 2025.
ista: Nessonov N, Ngo NT. 2025. Indecomposable characters of inductive limits of
symmetric groups. Representation Theory. 29(8), 256–288.
mla: Nessonov, Nikolay, and Nhok T. Ngo. “Indecomposable Characters of Inductive
Limits of Symmetric Groups.” Representation Theory, vol. 29, no. 8, American
Mathematical Society, 2025, pp. 256–88, doi:10.1090/ert/689.
short: N. Nessonov, N.T. Ngo, Representation Theory 29 (2025) 256–288.
corr_author: '1'
date_created: 2025-04-24T08:48:05Z
date_published: 2025-04-10T00:00:00Z
date_updated: 2025-05-05T06:59:07Z
day: '10'
ddc:
- '510'
department:
- _id: GradSch
- _id: TaHa
doi: 10.1090/ert/689
external_id:
arxiv:
- '2206.01964'
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checksum: f6541ea1736a7413c6d24f14d64a4dda
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file_date_updated: 2025-05-05T06:57:49Z
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intvolume: ' 29'
issue: '8'
language:
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license: https://creativecommons.org/licenses/by/3.0/
month: '04'
oa: 1
oa_version: Published Version
page: 256-288
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: Representation Theory
publication_identifier:
issn:
- 1088-4165
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Indecomposable characters of inductive limits of symmetric groups
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...
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_id: '20664'
abstract:
- lang: eng
text: Conference travel contributes to the climate footprint of academic research.
Here, we provide a quantitative estimate of the carbon emissions associated with
conference attendance by analyzing travel data from participants of 10 international
conferences in the field of magnetic resonance, namely EUROMAR, ENC and ICMRBS.
We find that attending a EUROMAR conference produces, on average, more than 1 t CO2 eq..
For the analyzed conferences outside Europe, the corresponding value is about
2–3 times higher, on average, with intercontinental trips amounting to up to 5 t.
We compare these conference-related emissions to other activities associated with
research and show that conference travel is a substantial portion of the total
climate footprint of a researcher in magnetic resonance. We explore several strategies
to reduce these emissions, including the impact of selecting conference venues
more strategically and the possibility of decentralized conferences. Through a
detailed comparison of train versus air travel – accounting for both direct and
infrastructure-related emissions – we demonstrate that train travel offers considerable
carbon savings. These data may provide a basis for strategic choices of future
conferences in the field and for individuals deciding on their conference attendance.
acknowledgement: 'First and foremost, we are grateful to the conference organizers
who have provided data, either in the form of tables or by pointing us to abstract
books. We thank the reviewers and the handling editor (Gottfried Otting) for the
careful reading and suggestions. This project emerged from an interactive course
about energy and climate, held at IST Austria by Jeroen Dobbelaere, Georgios Katsaros
and Paul Schanda. We are grateful to ISTA''s Graduate School for enabling this interdisciplinary
course and to all participating students. We thank the following persons for discussions
and/or comments about the manuscript: Helene Van Melckebeke, Mei Hong, Jeff Hoch,
Gottfried Otting and Matthias Ernst. For the preparation of the manuscript, AI tools
have been used, namely for finding relevant literature (ChatGPT) and for correcting
the text (Writefull, within Overleaf LaTeX).'
article_processing_charge: Yes
article_type: original
author:
- first_name: Lucky
full_name: Kapoor, Lucky
id: 84b9700b-15b2-11ec-abd3-831089e67615
last_name: Kapoor
orcid: 0000-0001-8319-2148
- first_name: Natalia
full_name: Ruzickova, Natalia
id: D2761128-D73D-11E9-A1BF-BA0DE6697425
last_name: Ruzickova
- first_name: Predrag
full_name: Zivadinovic, Predrag
id: 68AA0E5A-AFDA-11E9-9994-141DE6697425
last_name: Zivadinovic
- first_name: Valentin
full_name: Leitner, Valentin
id: 4c665ce3-0016-11ec-bea0-e44de7a4fa3d
last_name: Leitner
- first_name: Maria A
full_name: Sisak, Maria A
id: 44A03D04-AEA4-11E9-B225-EA2DE6697425
last_name: Sisak
- first_name: Cecelia N
full_name: Mweka, Cecelia N
id: 2a69ab4b-896a-11ed-bdf8-cb8641cf2b21
last_name: Mweka
- first_name: Jeroen A
full_name: Dobbelaere, Jeroen A
id: c15a5412-de82-11ed-b809-8dc1aa996e40
last_name: Dobbelaere
- first_name: Georgios
full_name: Katsaros, Georgios
id: 38DB5788-F248-11E8-B48F-1D18A9856A87
last_name: Katsaros
orcid: 0000-0001-8342-202X
- first_name: Paul
full_name: Schanda, Paul
id: 7B541462-FAF6-11E9-A490-E8DFE5697425
last_name: Schanda
orcid: 0000-0002-9350-7606
citation:
ama: 'Kapoor L, Ruzickova N, Zivadinovic P, et al. Quantifying the carbon footprint
of conference travel: The case of NMR meetings. Magnetic Resonance. 2025;6(2):243-256.
doi:10.5194/mr-6-243-2025'
apa: 'Kapoor, L., Ruzickova, N., Zivadinovic, P., Leitner, V., Sisak, M. A., Mweka,
C. N., … Schanda, P. (2025). Quantifying the carbon footprint of conference travel:
The case of NMR meetings. Magnetic Resonance. Copernicus Publications.
https://doi.org/10.5194/mr-6-243-2025'
chicago: 'Kapoor, Lucky, Natalia Ruzickova, Predrag Zivadinovic, Valentin Leitner,
Maria A Sisak, Cecelia N Mweka, Jeroen A Dobbelaere, Georgios Katsaros, and Paul
Schanda. “Quantifying the Carbon Footprint of Conference Travel: The Case of NMR
Meetings.” Magnetic Resonance. Copernicus Publications, 2025. https://doi.org/10.5194/mr-6-243-2025.'
ieee: 'L. Kapoor et al., “Quantifying the carbon footprint of conference
travel: The case of NMR meetings,” Magnetic Resonance, vol. 6, no. 2. Copernicus
Publications, pp. 243–256, 2025.'
ista: 'Kapoor L, Ruzickova N, Zivadinovic P, Leitner V, Sisak MA, Mweka CN, Dobbelaere
JA, Katsaros G, Schanda P. 2025. Quantifying the carbon footprint of conference
travel: The case of NMR meetings. Magnetic Resonance. 6(2), 243–256.'
mla: 'Kapoor, Lucky, et al. “Quantifying the Carbon Footprint of Conference Travel:
The Case of NMR Meetings.” Magnetic Resonance, vol. 6, no. 2, Copernicus
Publications, 2025, pp. 243–56, doi:10.5194/mr-6-243-2025.'
short: L. Kapoor, N. Ruzickova, P. Zivadinovic, V. Leitner, M.A. Sisak, C.N. Mweka,
J.A. Dobbelaere, G. Katsaros, P. Schanda, Magnetic Resonance 6 (2025) 243–256.
corr_author: '1'
date_created: 2025-11-23T23:01:39Z
date_published: 2025-11-10T00:00:00Z
date_updated: 2026-05-20T08:01:13Z
day: '10'
ddc:
- '000'
department:
- _id: JoFi
- _id: GaTk
- _id: JoCs
- _id: EvBe
- _id: TaHa
- _id: GradSch
- _id: GeKa
- _id: PaSc
doi: 10.5194/mr-6-243-2025
file:
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checksum: c63dd47b0e77f9451821436bb77d27c9
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creator: dernst
date_created: 2025-11-24T08:25:19Z
date_updated: 2025-11-24T08:25:19Z
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file_name: 2025_MagneticResonance_Kapoor.pdf
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intvolume: ' 6'
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month: '11'
oa: 1
oa_version: Published Version
page: 243-256
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Magnetic Resonance
publication_identifier:
eissn:
- 2699-0016
publication_status: published
publisher: Copernicus Publications
quality_controlled: '1'
related_material:
link:
- description: News on ISTA website
relation: research_data
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scopus_import: '1'
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title: 'Quantifying the carbon footprint of conference travel: The case of NMR meetings'
tmp:
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user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
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...
---
APC_amount: 2742,92 EUR
OA_place: publisher
OA_type: hybrid
_id: '18108'
abstract:
- lang: eng
text: Here we announce the construction and properties of a big commutative subalgebra
of the Kirillov algebra attached to a finite dimensional irreducible representation
of a complex semisimple Lie group. They are commutative finite flat algebras over
the cohomology of the classifying space of the group. They are isomorphic with
the equivariant intersection cohomology of affine Schubert varieties, endowing
the latter with a new ring structure. Study of the finer aspects of the structure
of the big algebras will also furnish the stalks of the intersection cohomology
with ring structure, thus ringifying Lusztig’s q-weight multiplicity polynomials
i.e., certain affine Kazhdan–Lusztig polynomials.
acknowledgement: "We thank Nigel Hitchin for discussions and the joint projects this
paper has grown out from. We thank Vladyslav Zveryk for collaboration on Theorem
2.3 and on the corresponding Magma code which implements big algebras. We thank
Hiraku Nakajima for discussions and pointing out Theorem 3.1.2, a result generalizing
our original observation in the= = 0 case. Special thanks go to Leonid Rybnikov
for patiently explaining his works, in particular crucial to Theorem 2.1. We thank
Michel Brion, Michael Finkelberg, Oscar García-Prada, Jakub Löwit, Joel Kamnitzer,
Friedrich Knop, Michael McBreen, Anton Mellit, Takuro Mochizuki, Shon Ngô, Kamil
Rychlewicz, Shiyu Shen, Leslie Spencer, Balázs Szendr ˝ oi, András Szenes, and Oksana\r\nYakimova
for comments and discussions. Kamil Rychlewicz and Daniel Bedats helped with the
Mathematica files for the figures, and we used the SM_isospin Tikz package of Izaak
Neutelings for drawing the baryon multiplets. We thank the referees for many useful
comments. We acknowledge funding from FWF grant “Geometry of the tip of the global
nilpotent cone” no. P 35847."
article_number: e2319341121
article_processing_charge: Yes (in subscription journal)
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
citation:
ama: Hausel T. Commutative avatars of representations of semisimple Lie groups.
Proceedings of the National Academy of Sciences of the United States of America.
2024;121(38). doi:10.1073/pnas.2319341121
apa: Hausel, T. (2024). Commutative avatars of representations of semisimple Lie
groups. Proceedings of the National Academy of Sciences of the United States
of America. National Academy of Sciences. https://doi.org/10.1073/pnas.2319341121
chicago: Hausel, Tamás. “Commutative Avatars of Representations of Semisimple Lie
Groups.” Proceedings of the National Academy of Sciences of the United States
of America. National Academy of Sciences, 2024. https://doi.org/10.1073/pnas.2319341121.
ieee: T. Hausel, “Commutative avatars of representations of semisimple Lie groups,”
Proceedings of the National Academy of Sciences of the United States of America,
vol. 121, no. 38. National Academy of Sciences, 2024.
ista: Hausel T. 2024. Commutative avatars of representations of semisimple Lie groups.
Proceedings of the National Academy of Sciences of the United States of America.
121(38), e2319341121.
mla: Hausel, Tamás. “Commutative Avatars of Representations of Semisimple Lie Groups.”
Proceedings of the National Academy of Sciences of the United States of America,
vol. 121, no. 38, e2319341121, National Academy of Sciences, 2024, doi:10.1073/pnas.2319341121.
short: T. Hausel, Proceedings of the National Academy of Sciences of the United
States of America 121 (2024).
corr_author: '1'
date_created: 2024-09-22T22:01:41Z
date_published: 2024-09-17T00:00:00Z
date_updated: 2025-05-08T09:57:59Z
day: '17'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1073/pnas.2319341121
external_id:
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- '39259592'
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has_accepted_license: '1'
intvolume: ' 121'
issue: '38'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: Proceedings of the National Academy of Sciences of the United States
of America
publication_identifier:
eissn:
- 1091-6490
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- relation: press_release
url: https://ista.ac.at/en/news/big-algebras-a-dictionary-of-abstract-math/
scopus_import: '1'
status: public
title: Commutative avatars of representations of semisimple Lie groups
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short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 121
year: '2024'
...
---
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
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
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:
- access_level: closed
checksum: 1610063569f5452f8a5acef728c2fc26
content_type: application/zip
creator: krychlew
date_created: 2024-06-26T20:56:27Z
date_updated: 2024-06-26T21:00:14Z
file_id: '17179'
file_name: thesis.zip
file_size: 2761814
relation: source_file
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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'
...