---
_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
- first_name: Michael Lennox
full_name: Wong, Michael Lennox
last_name: Wong
- first_name: Dimitri
full_name: Wyss, Dimitri
last_name: Wyss
citation:
ama: Hausel T, Wong ML, Wyss D. Arithmetic and metric aspects of open de Rham spaces.
Proceedings of the London Mathematical Society. 2023;127(4):958-1027. doi:10.1112/plms.12555
apa: Hausel, T., Wong, M. L., & Wyss, D. (2023). Arithmetic and metric aspects
of open de Rham spaces. Proceedings of the London Mathematical Society.
Wiley. https://doi.org/10.1112/plms.12555
chicago: Hausel, Tamás, Michael Lennox Wong, and Dimitri Wyss. “Arithmetic and Metric
Aspects of Open de Rham Spaces.” Proceedings of the London Mathematical Society.
Wiley, 2023. https://doi.org/10.1112/plms.12555.
ieee: T. Hausel, M. L. Wong, and D. Wyss, “Arithmetic and metric aspects of open
de Rham spaces,” Proceedings of the London Mathematical Society, vol. 127,
no. 4. Wiley, pp. 958–1027, 2023.
ista: Hausel T, Wong ML, Wyss D. 2023. Arithmetic and metric aspects of open de
Rham spaces. Proceedings of the London Mathematical Society. 127(4), 958–1027.
mla: Hausel, Tamás, et al. “Arithmetic and Metric Aspects of Open de Rham Spaces.”
Proceedings of the London Mathematical Society, vol. 127, no. 4, Wiley,
2023, pp. 958–1027, doi:10.1112/plms.12555.
short: T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society
127 (2023) 958–1027.
date_created: 2023-08-27T22:01:18Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2024-01-30T12:56:10Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/plms.12555
ec_funded: 1
external_id:
arxiv:
- '1807.04057'
isi:
- '001049312700001'
file:
- access_level: open_access
checksum: 2af4d2d6a8ae42f7d3fba0188e79ae82
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:56:00Z
date_updated: 2024-01-30T12:56:00Z
file_id: '14910'
file_name: 2023_ProcLondonMathSoc_Hausel.pdf
file_size: 651335
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:56:00Z
has_accepted_license: '1'
intvolume: ' 127'
isi: 1
issue: '4'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 958-1027
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
- _id: 25E6C798-B435-11E9-9278-68D0E5697425
grant_number: '153627'
name: Arithmetic quantization of character and quiver varities
publication: Proceedings of the London Mathematical Society
publication_identifier:
eissn:
- 1460-244X
issn:
- 0024-6115
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic and metric aspects of open de Rham spaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 127
year: '2023'
...
---
_id: '12303'
abstract:
- lang: eng
text: We construct for each choice of a quiver Q, a cohomology theory A, and a poset
P a “loop Grassmannian” GP(Q,A). This generalizes loop Grassmannians of semisimple
groups and the loop Grassmannians of based quadratic forms. The addition of a
“dilation” torus D⊆G2m gives a quantization GPD(Q,A). This construction is motivated
by the program of introducing an inner cohomology theory in algebraic geometry
adequate for the Geometric Langlands program (Mirković, Some extensions of the
notion of loop Grassmannians. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardešić
issue. No. 532, 53–74, 2017) and on the construction of affine quantum groups
from generalized cohomology theories (Yang and Zhao, Quiver varieties and elliptic
quantum groups, preprint. arxiv1708.01418).
acknowledgement: I.M. thanks Zhijie Dong for long-term discussions on the material
that entered this work. We thank Misha Finkelberg for pointing out errors in earlier
versions. His advice and his insistence have led to a much better paper. A part
of the writing was done at the conference at IST (Vienna) attended by all coauthors.
We therefore thank the organizers of the conference and the support of ERC Advanced
Grant Arithmetic and Physics of Higgs moduli spaces No. 320593. The work of I.M.
was partially supported by NSF grants. The work of Y.Y. was partially supported
by the Australian Research Council (ARC) via the award DE190101231. The work of
G.Z. was partially supported by ARC via the award DE190101222.
alternative_title:
- Trends in Mathematics
article_processing_charge: No
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: 2023-01-27T07:07:31Z
day: '16'
department:
- _id: TaHa
doi: 10.1007/978-3-030-82007-7_8
ec_funded: 1
edition: '1'
editor:
- first_name: Vladimir
full_name: Baranovskky, Vladimir
last_name: Baranovskky
- first_name: Nicolas
full_name: Guay, Nicolas
last_name: Guay
- first_name: Travis
full_name: Schedler, Travis
last_name: Schedler
external_id:
arxiv:
- '1810.10095'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1810.10095
month: '06'
oa: 1
oa_version: Preprint
page: 347-392
place: Cham
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Representation Theory and Algebraic Geometry
publication_identifier:
eisbn:
- '9783030820077'
eissn:
- 2297-024X
isbn:
- '9783030820060'
issn:
- 2297-0215
publication_status: published
publisher: Springer Nature; Birkhäuser
quality_controlled: '1'
scopus_import: '1'
series_title: TM
status: public
title: Loop Grassmannians of Quivers and Affine Quantum Groups
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '9359'
abstract:
- lang: eng
text: "We prove that the factorization homologies of a scheme with coefficients
in truncated polynomial algebras compute the cohomologies of its generalized configuration
spaces. Using Koszul duality between commutative algebras and Lie algebras, we
obtain new expressions for the cohomologies of the latter. As a consequence, we
obtain a uniform and conceptual approach for treating homological stability, homological
densities, and arithmetic densities of generalized configuration spaces. Our results
categorify, generalize, and in fact provide a conceptual understanding of the
coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of
the stable homological densities also yields rational homotopy types, answering
a question posed by Vakil--Wood. Our approach hinges on the study of homological
stability of cohomological Chevalley complexes, which is of independent interest.\r\n"
acknowledgement: "This paper owes an obvious intellectual debt to the illuminating
treatments of factorization homology by J.\r\nFrancis, D. Gaitsgory, and J. Lurie
in [GL,G1, FG]. The author would like to thank B. Farb and J. Wolfson for\r\nbringing
the question of explaining coincidences in homological densities to his attention.
Moreover, the author\r\nthanks J. Wolfson for many helpful conversations on the
subject, O. Randal-Williams for many comments which\r\ngreatly help improve the
exposition, and G. C. Drummond-Cole for many useful conversations on L∞-algebras.\r\nFinally,
the author is grateful to the anonymous referee for carefully reading the manuscript
and for providing\r\nnumerous comments which greatly helped improve the clarity
and precision of the exposition.\r\nThis work is supported by the Advanced Grant
“Arithmetic and Physics of Higgs moduli spaces” No. 320593 of\r\nthe European Research
Council and the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization\r\nHomology,”
Austrian Science Fund (FWF): M 2751."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Quoc P
full_name: Ho, Quoc P
id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
last_name: Ho
citation:
ama: Ho QP. Homological stability and densities of generalized configuration spaces.
Geometry & Topology. 2021;25(2):813-912. doi:10.2140/gt.2021.25.813
apa: Ho, Q. P. (2021). Homological stability and densities of generalized configuration
spaces. Geometry & Topology. Mathematical Sciences Publishers. https://doi.org/10.2140/gt.2021.25.813
chicago: Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration
Spaces.” Geometry & Topology. Mathematical Sciences Publishers, 2021.
https://doi.org/10.2140/gt.2021.25.813.
ieee: Q. P. Ho, “Homological stability and densities of generalized configuration
spaces,” Geometry & Topology, vol. 25, no. 2. Mathematical Sciences
Publishers, pp. 813–912, 2021.
ista: Ho QP. 2021. Homological stability and densities of generalized configuration
spaces. Geometry & Topology. 25(2), 813–912.
mla: Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration
Spaces.” Geometry & Topology, vol. 25, no. 2, Mathematical Sciences
Publishers, 2021, pp. 813–912, doi:10.2140/gt.2021.25.813.
short: Q.P. Ho, Geometry & Topology 25 (2021) 813–912.
date_created: 2021-05-02T06:59:33Z
date_published: 2021-04-27T00:00:00Z
date_updated: 2023-08-08T13:28:59Z
day: '27'
ddc:
- '514'
- '516'
- '512'
department:
- _id: TaHa
doi: 10.2140/gt.2021.25.813
ec_funded: 1
external_id:
arxiv:
- '1802.07948'
isi:
- '000682738600005'
file:
- access_level: open_access
checksum: 643a8d2d6f06f0888dcd7503f55d0920
content_type: application/pdf
creator: qho
date_created: 2021-05-03T06:54:06Z
date_updated: 2021-05-03T06:54:06Z
file_id: '9366'
file_name: densities.pdf
file_size: 479268
relation: main_file
success: 1
file_date_updated: 2021-05-03T06:54:06Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
issue: '2'
keyword:
- Generalized configuration spaces
- homological stability
- homological densities
- chiral algebras
- chiral homology
- factorization algebras
- Koszul duality
- Ran space
language:
- iso: eng
month: '04'
oa: 1
oa_version: Submitted Version
page: 813-912
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
- _id: 26B96266-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02751
name: Algebro-Geometric Applications of Factorization Homology
publication: Geometry & Topology
publication_identifier:
issn:
- 1364-0380
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
status: public
title: Homological stability and densities of generalized configuration spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2021'
...
---
_id: '7940'
abstract:
- lang: eng
text: We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody
Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter
is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras.
As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this
class of affine Yangians. Another independent proof of the PBW theorem is given
recently by Guay, Regelskis, and Wendlandt [GRW18].
acknowledgement: Gufang Zhao is affiliated to IST Austria, Hausel group until July
of 2018. Supported by the Advanced Grant Arithmetic and Physics of Higgs moduli
spaces No. 320593 of the European Research Council.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yaping
full_name: Yang, Yaping
id: 360D8648-F248-11E8-B48F-1D18A9856A87
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Yang Y, Zhao G. The PBW theorem for affine Yangians. Transformation Groups.
2020;25:1371-1385. doi:10.1007/s00031-020-09572-6
apa: Yang, Y., & Zhao, G. (2020). The PBW theorem for affine Yangians. Transformation
Groups. Springer Nature. https://doi.org/10.1007/s00031-020-09572-6
chicago: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” Transformation
Groups. Springer Nature, 2020. https://doi.org/10.1007/s00031-020-09572-6.
ieee: Y. Yang and G. Zhao, “The PBW theorem for affine Yangians,” Transformation
Groups, vol. 25. Springer Nature, pp. 1371–1385, 2020.
ista: Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation
Groups. 25, 1371–1385.
mla: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” Transformation
Groups, vol. 25, Springer Nature, 2020, pp. 1371–85, doi:10.1007/s00031-020-09572-6.
short: Y. Yang, G. Zhao, Transformation Groups 25 (2020) 1371–1385.
date_created: 2020-06-07T22:00:55Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2023-08-21T07:06:21Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00031-020-09572-6
ec_funded: 1
external_id:
arxiv:
- '1804.04375'
isi:
- '000534874300003'
intvolume: ' 25'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.04375
month: '12'
oa: 1
oa_version: Preprint
page: 1371-1385
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Transformation Groups
publication_identifier:
eissn:
- 1531586X
issn:
- '10834362'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The PBW theorem for affine Yangians
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2020'
...
---
_id: '7004'
abstract:
- lang: eng
text: We define an action of the (double of) Cohomological Hall algebra of Kontsevich
and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov.
We identify this action with the one of the affine Yangian of gl(1). Based on
that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák.
We conjecture that our approach works for a big class of Calabi–Yau categories,
including those associated with toric Calabi–Yau 3-folds.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Miroslav
full_name: Rapcak, Miroslav
last_name: Rapcak
- first_name: Yan
full_name: Soibelman, Yan
last_name: Soibelman
- first_name: Yaping
full_name: Yang, Yaping
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex
algebras and instantons. Communications in Mathematical Physics. 2020;376:1803-1873.
doi:10.1007/s00220-019-03575-5
apa: Rapcak, M., Soibelman, Y., Yang, Y., & Zhao, G. (2020). Cohomological Hall
algebras, vertex algebras and instantons. Communications in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s00220-019-03575-5
chicago: Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological
Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical
Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03575-5.
ieee: M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras,
vertex algebras and instantons,” Communications in Mathematical Physics,
vol. 376. Springer Nature, pp. 1803–1873, 2020.
ista: Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras,
vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873.
mla: Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and
Instantons.” Communications in Mathematical Physics, vol. 376, Springer
Nature, 2020, pp. 1803–73, doi:10.1007/s00220-019-03575-5.
short: M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical
Physics 376 (2020) 1803–1873.
date_created: 2019-11-12T14:01:27Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-17T14:02:59Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00220-019-03575-5
ec_funded: 1
external_id:
arxiv:
- '1810.10402'
isi:
- '000536255500004'
intvolume: ' 376'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1810.10402
month: '06'
oa: 1
oa_version: Preprint
page: 1803-1873
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Cohomological Hall algebras, vertex algebras and instantons
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 376
year: '2020'
...
---
_id: '6986'
abstract:
- lang: eng
text: 'Li-Nadler proposed a conjecture about traces of Hecke categories, which implies
the semistable part of the Betti geometric Langlands conjecture of Ben-Zvi-Nadler
in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds
in the natural generality of reflection groups in Euclidean or hyperbolic space.
As a corollary, we give an expression of the centralizer of a finite order element
in a reflection group using homotopy theory. '
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Penghui
full_name: Li, Penghui
id: 42A24CCC-F248-11E8-B48F-1D18A9856A87
last_name: Li
citation:
ama: Li P. A colimit of traces of reflection groups. Proceedings of the American
Mathematical Society. 2019;147(11):4597-4604. doi:10.1090/proc/14586
apa: Li, P. (2019). A colimit of traces of reflection groups. Proceedings of
the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14586
chicago: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings
of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14586.
ieee: P. Li, “A colimit of traces of reflection groups,” Proceedings of the American
Mathematical Society, vol. 147, no. 11. AMS, pp. 4597–4604, 2019.
ista: Li P. 2019. A colimit of traces of reflection groups. Proceedings of the American
Mathematical Society. 147(11), 4597–4604.
mla: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings of
the American Mathematical Society, vol. 147, no. 11, AMS, 2019, pp. 4597–604,
doi:10.1090/proc/14586.
short: P. Li, Proceedings of the American Mathematical Society 147 (2019) 4597–4604.
date_created: 2019-11-04T16:10:50Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-09-05T12:22:21Z
day: '01'
department:
- _id: TaHa
doi: 10.1090/proc/14586
ec_funded: 1
external_id:
arxiv:
- '1810.07039'
isi:
- '000488621700004'
intvolume: ' 147'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1810.07039
month: '11'
oa: 1
oa_version: Preprint
page: 4597-4604
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: AMS
quality_controlled: '1'
scopus_import: '1'
status: public
title: A colimit of traces of reflection groups
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 147
year: '2019'
...
---
_id: '439'
abstract:
- lang: eng
text: "We count points over a finite field on wild character varieties,of Riemann
surfaces for singularities with regular semisimple leading term. The new feature
in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras.
Our result leads to the conjecture that the mixed Hodge polynomials of these character
varieties agree with previously conjectured perverse Hodge polynomials of certain
twisted parabolic Higgs moduli spaces, indicating the\r\npossibility of a P =
W conjecture for a suitable wild Hitchin system."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tamas
full_name: Hausel, Tamas
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Martin
full_name: Mereb, Martin
id: 43D735EE-F248-11E8-B48F-1D18A9856A87
last_name: Mereb
- first_name: Michael
full_name: Wong, Michael
last_name: Wong
citation:
ama: Hausel T, Mereb M, Wong M. Arithmetic and representation theory of wild character
varieties. Journal of the European Mathematical Society. 2019;21(10):2995-3052.
doi:10.4171/JEMS/896
apa: Hausel, T., Mereb, M., & Wong, M. (2019). Arithmetic and representation
theory of wild character varieties. Journal of the European Mathematical Society.
European Mathematical Society. https://doi.org/10.4171/JEMS/896
chicago: Hausel, Tamás, Martin Mereb, and Michael Wong. “Arithmetic and Representation
Theory of Wild Character Varieties.” Journal of the European Mathematical Society.
European Mathematical Society, 2019. https://doi.org/10.4171/JEMS/896.
ieee: T. Hausel, M. Mereb, and M. Wong, “Arithmetic and representation theory of
wild character varieties,” Journal of the European Mathematical Society,
vol. 21, no. 10. European Mathematical Society, pp. 2995–3052, 2019.
ista: Hausel T, Mereb M, Wong M. 2019. Arithmetic and representation theory of wild
character varieties. Journal of the European Mathematical Society. 21(10), 2995–3052.
mla: Hausel, Tamás, et al. “Arithmetic and Representation Theory of Wild Character
Varieties.” Journal of the European Mathematical Society, vol. 21, no.
10, European Mathematical Society, 2019, pp. 2995–3052, doi:10.4171/JEMS/896.
short: T. Hausel, M. Mereb, M. Wong, Journal of the European Mathematical Society
21 (2019) 2995–3052.
date_created: 2018-12-11T11:46:29Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-08-24T14:24:49Z
day: '01'
department:
- _id: TaHa
doi: 10.4171/JEMS/896
ec_funded: 1
external_id:
arxiv:
- '1604.03382'
isi:
- '000480413600002'
intvolume: ' 21'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1604.03382
month: '10'
oa: 1
oa_version: Preprint
page: 2995-3052
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Journal of the European Mathematical Society
publication_identifier:
eissn:
- 1435-9855
publication_status: published
publisher: European Mathematical Society
publist_id: '7384'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic and representation theory of wild character varieties
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 21
year: '2019'
...
---
_id: '322'
abstract:
- lang: eng
text: We construct quantizations of multiplicative hypertoric varieties using an
algebra of q-difference operators on affine space, where q is a root of unity
in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the
multiplicative hypertoric variety and admits an explicit finite étale splitting.
The global sections of this Azumaya algebra is a hypertoric quantum group, and
we prove a localization theorem. We introduce a general framework of Frobenius
quantum moment maps and their Hamiltonian reductions; our results shed light on
an instance of this framework.
acknowledgement: "National Science Foundation: Graduate Research Fellowship and grant
No.0932078000; ERC Advanced Grant “Arithmetic and Physics of Higgs moduli spaces”
No. 320593 \r\nThe author is grateful to David Jordan for suggesting this project
and providing guidance throughout, particularly for the formulation of Frobenius
quantum moment maps and key ideas in the proofs of Theorems 3.12 and 4.8. Special
thanks to David Ben-Zvi (the author's PhD advisor) for numerous discussions and
constant encouragement, and for suggesting the term ‘hypertoric quantum group.’
Many results appearing in the current paper were proven independently by Nicholas
Cooney; the author is grateful to Nicholas for sharing his insight on various topics,
including Proposition 3.8. The author also thanks Nicholas Proudfoot for relating
the definition of multiplicative hypertoric varieties, as well as the content of
Remark 2.14. The author also benefited immensely from the close reading and detailed
comments of an anonymous referee, and from conversations with Justin Hilburn, Kobi
Kremnitzer, Michael McBreen, Tom Nevins, Travis Schedler, and Ben Webster. \r\n\r\n\r\n\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Iordan V
full_name: Ganev, Iordan V
id: 447491B8-F248-11E8-B48F-1D18A9856A87
last_name: Ganev
citation:
ama: Ganev IV. Quantizations of multiplicative hypertoric varieties at a root of
unity. Journal of Algebra. 2018;506:92-128. doi:10.1016/j.jalgebra.2018.03.015
apa: Ganev, I. V. (2018). Quantizations of multiplicative hypertoric varieties at
a root of unity. Journal of Algebra. World Scientific Publishing. https://doi.org/10.1016/j.jalgebra.2018.03.015
chicago: Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties
at a Root of Unity.” Journal of Algebra. World Scientific Publishing, 2018.
https://doi.org/10.1016/j.jalgebra.2018.03.015.
ieee: I. V. Ganev, “Quantizations of multiplicative hypertoric varieties at a root
of unity,” Journal of Algebra, vol. 506. World Scientific Publishing, pp.
92–128, 2018.
ista: Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a
root of unity. Journal of Algebra. 506, 92–128.
mla: Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a
Root of Unity.” Journal of Algebra, vol. 506, World Scientific Publishing,
2018, pp. 92–128, doi:10.1016/j.jalgebra.2018.03.015.
short: I.V. Ganev, Journal of Algebra 506 (2018) 92–128.
date_created: 2018-12-11T11:45:49Z
date_published: 2018-07-15T00:00:00Z
date_updated: 2023-09-15T12:08:38Z
day: '15'
department:
- _id: TaHa
doi: 10.1016/j.jalgebra.2018.03.015
ec_funded: 1
external_id:
arxiv:
- '1412.7211'
isi:
- '000433270600005'
intvolume: ' 506'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1412.7211
month: '07'
oa: 1
oa_version: Preprint
page: 92 - 128
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Journal of Algebra
publication_status: published
publisher: World Scientific Publishing
publist_id: '7543'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantizations of multiplicative hypertoric varieties at a root of unity
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 506
year: '2018'
...
---
_id: '687'
abstract:
- lang: eng
text: Pursuing the similarity between the Kontsevich-Soibelman construction of the
cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of
canonical bases for quantum enveloping algebras, and the similarity between the
integrality conjecture for motivic Donaldson-Thomas invariants and the PBW theorem
for quantum enveloping algebras, we build a coproduct on the CoHA associated to
a quiver with potential. We also prove a cohomological dimensional reduction theorem,
further linking a special class of CoHAs with Yangians, and explaining how to
connect the study of character varieties with the study of CoHAs.
author:
- first_name: Ben
full_name: Davison, Ben
id: 4634AB1E-F248-11E8-B48F-1D18A9856A87
last_name: Davison
orcid: 0000-0002-8944-4390
citation:
ama: Davison B. The critical CoHA of a quiver with potential. Quarterly Journal
of Mathematics. 2017;68(2):635-703. doi:10.1093/qmath/haw053
apa: Davison, B. (2017). The critical CoHA of a quiver with potential. Quarterly
Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qmath/haw053
chicago: Davison, Ben. “The Critical CoHA of a Quiver with Potential.” Quarterly
Journal of Mathematics. Oxford University Press, 2017. https://doi.org/10.1093/qmath/haw053.
ieee: B. Davison, “The critical CoHA of a quiver with potential,” Quarterly Journal
of Mathematics, vol. 68, no. 2. Oxford University Press, pp. 635–703, 2017.
ista: Davison B. 2017. The critical CoHA of a quiver with potential. Quarterly Journal
of Mathematics. 68(2), 635–703.
mla: Davison, Ben. “The Critical CoHA of a Quiver with Potential.” Quarterly
Journal of Mathematics, vol. 68, no. 2, Oxford University Press, 2017, pp.
635–703, doi:10.1093/qmath/haw053.
short: B. Davison, Quarterly Journal of Mathematics 68 (2017) 635–703.
date_created: 2018-12-11T11:47:55Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2021-01-12T08:09:24Z
day: '01'
department:
- _id: TaHa
doi: 10.1093/qmath/haw053
ec_funded: 1
intvolume: ' 68'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1311.7172
month: '06'
oa: 1
oa_version: Submitted Version
page: 635 - 703
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Quarterly Journal of Mathematics
publication_identifier:
issn:
- '00335606'
publication_status: published
publisher: Oxford University Press
publist_id: '7022'
quality_controlled: '1'
scopus_import: 1
status: public
title: The critical CoHA of a quiver with potential
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2017'
...