---
_id: '8539'
abstract:
- lang: eng
text: Cohomological and K-theoretic stable bases originated from the study of quantum
cohomology and quantum K-theory. Restriction formula for cohomological stable
bases played an important role in computing the quantum connection of cotangent
bundle of partial flag varieties. In this paper we study the K-theoretic stable
bases of cotangent bundles of flag varieties. We describe these bases in terms
of the action of the affine Hecke algebra and the twisted group algebra of KostantKumar.
Using this algebraic description and the method of root polynomials, we give a
restriction formula of the stable bases. We apply it to obtain the restriction
formula for partial flag varieties. We also build a relation between the stable
basis and the Casselman basis in the principal series representations of the Langlands
dual group. As an application, we give a closed formula for the transition matrix
between Casselman basis and the characteristic functions.
- lang: fre
text: "Les bases stables cohomologiques et K-théoriques proviennent de l’étude de
la cohomologie quantique et de la K-théorie quantique. La formule de restriction
pour les bases stables cohomologiques a joué un rôle important dans le calcul
de la connexion quantique du fibré cotangent de variétés de drapeaux partielles.
Dans cet article, nous étudions les bases stables K-théoriques de fibré cotangents
des variétés de drapeaux. Nous décrivons ces bases en fonction de l’action de
l’algèbre de Hecke affine et de l’algèbre de Kostant-Kumar. En utilisant cette
description algébrique et la méthode des polynômes de racine, nous donnons une
formule de restriction des bases stables. Nous l’appliquons\r\npour obtenir la
formule de restriction pour les variétés de drapeaux partielles. Nous construisons
également une relation entre la base stable et la base de Casselman dans les représentations
de la série principale du groupe dual de Langlands p-adique. Comme une application,
nous donnons une formule close pour la matrice de transition entre la base de
Casselman et les fonctions caractéristiques. "
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: C.
full_name: Su, C.
last_name: Su
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
- first_name: C.
full_name: Zhong, C.
last_name: Zhong
citation:
ama: Su C, Zhao G, Zhong C. On the K-theory stable bases of the springer resolution.
Annales Scientifiques de l’Ecole Normale Superieure. 2020;53(3):663-671.
doi:10.24033/asens.2431
apa: Su, C., Zhao, G., & Zhong, C. (2020). On the K-theory stable bases of the
springer resolution. Annales Scientifiques de l’Ecole Normale Superieure.
Société Mathématique de France. https://doi.org/10.24033/asens.2431
chicago: Su, C., Gufang Zhao, and C. Zhong. “On the K-Theory Stable Bases of the
Springer Resolution.” Annales Scientifiques de l’Ecole Normale Superieure.
Société Mathématique de France, 2020. https://doi.org/10.24033/asens.2431.
ieee: C. Su, G. Zhao, and C. Zhong, “On the K-theory stable bases of the springer
resolution,” Annales Scientifiques de l’Ecole Normale Superieure, vol.
53, no. 3. Société Mathématique de France, pp. 663–671, 2020.
ista: Su C, Zhao G, Zhong C. 2020. On the K-theory stable bases of the springer
resolution. Annales Scientifiques de l’Ecole Normale Superieure. 53(3), 663–671.
mla: Su, C., et al. “On the K-Theory Stable Bases of the Springer Resolution.” Annales
Scientifiques de l’Ecole Normale Superieure, vol. 53, no. 3, Société Mathématique
de France, 2020, pp. 663–71, doi:10.24033/asens.2431.
short: C. Su, G. Zhao, C. Zhong, Annales Scientifiques de l’Ecole Normale Superieure
53 (2020) 663–671.
date_created: 2020-09-20T22:01:38Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-22T09:27:57Z
day: '01'
department:
- _id: TaHa
doi: 10.24033/asens.2431
external_id:
arxiv:
- '1708.08013'
isi:
- '000592182600004'
intvolume: ' 53'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.08013
month: '06'
oa: 1
oa_version: Preprint
page: 663-671
publication: Annales Scientifiques de l'Ecole Normale Superieure
publication_identifier:
issn:
- 0012-9593
publication_status: published
publisher: Société Mathématique de France
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the K-theory stable bases of the springer resolution
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2020'
...
---
_id: '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: '7683'
abstract:
- lang: eng
text: For any free oriented Borel–Moore homology theory A, we construct an associative
product on the A-theory of the stack of Higgs torsion sheaves over a projective
curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation,
and prove it is faithful when A is replaced with usual Borel–Moore homology groups.
We also introduce moduli spaces of stable triples, heavily inspired by Nakajima
quiver varieties, whose A-theory admits an AHa0C-action. These triples can be
interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action
of AHa0C on the cohomology of Hilbert schemes of points on T∗C.
article_number: '30'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Sasha
full_name: Minets, Sasha
id: 3E7C5304-F248-11E8-B48F-1D18A9856A87
last_name: Minets
orcid: 0000-0003-3883-1806
citation:
ama: Minets S. Cohomological Hall algebras for Higgs torsion sheaves, moduli of
triples and sheaves on surfaces. Selecta Mathematica, New Series. 2020;26(2).
doi:10.1007/s00029-020-00553-x
apa: Minets, S. (2020). Cohomological Hall algebras for Higgs torsion sheaves, moduli
of triples and sheaves on surfaces. Selecta Mathematica, New Series. Springer
Nature. https://doi.org/10.1007/s00029-020-00553-x
chicago: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves,
Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series.
Springer Nature, 2020. https://doi.org/10.1007/s00029-020-00553-x.
ieee: S. Minets, “Cohomological Hall algebras for Higgs torsion sheaves, moduli
of triples and sheaves on surfaces,” Selecta Mathematica, New Series, vol.
26, no. 2. Springer Nature, 2020.
ista: Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli
of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2), 30.
mla: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli
of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series, vol.
26, no. 2, 30, Springer Nature, 2020, doi:10.1007/s00029-020-00553-x.
short: S. Minets, Selecta Mathematica, New Series 26 (2020).
date_created: 2020-04-26T22:00:44Z
date_published: 2020-04-15T00:00:00Z
date_updated: 2023-08-21T06:14:58Z
day: '15'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00029-020-00553-x
external_id:
arxiv:
- '1801.01429'
isi:
- '000526036400001'
file:
- access_level: open_access
checksum: 2368c4662629b4759295eb365323b2ad
content_type: application/pdf
creator: dernst
date_created: 2020-04-28T10:57:58Z
date_updated: 2020-07-14T12:48:02Z
file_id: '7690'
file_name: 2020_SelectaMathematica_Minets.pdf
file_size: 792469
relation: main_file
file_date_updated: 2020-07-14T12:48:02Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Selecta Mathematica, New Series
publication_identifier:
eissn:
- '14209020'
issn:
- '10221824'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and
sheaves on surfaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 26
year: '2020'
...
---
_id: '196'
abstract:
- lang: eng
text: 'The abelian sandpile serves as a model to study self-organized criticality,
a phenomenon occurring in biological, physical and social processes. The identity
of the abelian group is a fractal composed of self-similar patches, and its limit
is subject of extensive collaborative research. Here, we analyze the evolution
of the sandpile identity under harmonic fields of different orders. We show that
this evolution corresponds to periodic cycles through the abelian group characterized
by the smooth transformation and apparent conservation of the patches constituting
the identity. The dynamics induced by second and third order harmonics resemble
smooth stretchings, respectively translations, of the identity, while the ones
induced by fourth order harmonics resemble magnifications and rotations. Starting
with order three, the dynamics pass through extended regions of seemingly random
configurations which spontaneously reassemble into accentuated patterns. We show
that the space of harmonic functions projects to the extended analogue of the
sandpile group, thus providing a set of universal coordinates identifying configurations
between different domains. Since the original sandpile group is a subgroup of
the extended one, this directly implies that it admits a natural renormalization.
Furthermore, we show that the harmonic fields can be induced by simple Markov
processes, and that the corresponding stochastic dynamics show remarkable robustness
over hundreds of periods. Finally, we encode information into seemingly random
configurations, and decode this information with an algorithm requiring minimal
prior knowledge. Our results suggest that harmonic fields might split the sandpile
group into sub-sets showing different critical coefficients, and that it might
be possible to extend the fractal structure of the identity beyond the boundaries
of its domain. '
acknowledgement: "M.L. is grateful to the members of the C Guet and G Tkacik groups
for valuable comments and support. M.S. is grateful to Nikita Kalinin for inspiring
communications.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Moritz
full_name: Lang, Moritz
id: 29E0800A-F248-11E8-B48F-1D18A9856A87
last_name: Lang
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
citation:
ama: Lang M, Shkolnikov M. Harmonic dynamics of the Abelian sandpile. Proceedings
of the National Academy of Sciences. 2019;116(8):2821-2830. doi:10.1073/pnas.1812015116
apa: Lang, M., & Shkolnikov, M. (2019). Harmonic dynamics of the Abelian sandpile.
Proceedings of the National Academy of Sciences. National Academy of Sciences.
https://doi.org/10.1073/pnas.1812015116
chicago: Lang, Moritz, and Mikhail Shkolnikov. “Harmonic Dynamics of the Abelian
Sandpile.” Proceedings of the National Academy of Sciences. National Academy
of Sciences, 2019. https://doi.org/10.1073/pnas.1812015116.
ieee: M. Lang and M. Shkolnikov, “Harmonic dynamics of the Abelian sandpile,” Proceedings
of the National Academy of Sciences, vol. 116, no. 8. National Academy of
Sciences, pp. 2821–2830, 2019.
ista: Lang M, Shkolnikov M. 2019. Harmonic dynamics of the Abelian sandpile. Proceedings
of the National Academy of Sciences. 116(8), 2821–2830.
mla: Lang, Moritz, and Mikhail Shkolnikov. “Harmonic Dynamics of the Abelian Sandpile.”
Proceedings of the National Academy of Sciences, vol. 116, no. 8, National
Academy of Sciences, 2019, pp. 2821–30, doi:10.1073/pnas.1812015116.
short: M. Lang, M. Shkolnikov, Proceedings of the National Academy of Sciences 116
(2019) 2821–2830.
date_created: 2018-12-11T11:45:08Z
date_published: 2019-02-19T00:00:00Z
date_updated: 2023-09-11T14:09:34Z
day: '19'
department:
- _id: CaGu
- _id: GaTk
- _id: TaHa
doi: 10.1073/pnas.1812015116
external_id:
arxiv:
- '1806.10823'
isi:
- '000459074400013'
pmid:
- ' 30728300'
intvolume: ' 116'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1073/pnas.1812015116
month: '02'
oa: 1
oa_version: Published Version
page: 2821-2830
pmid: 1
publication: Proceedings of the National Academy of Sciences
publication_identifier:
eissn:
- 1091-6490
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- description: News on IST Webpage
relation: press_release
url: https://ist.ac.at/en/news/famous-sandpile-model-shown-to-move-like-a-traveling-sand-dune/
scopus_import: '1'
status: public
title: Harmonic dynamics of the Abelian sandpile
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 116
year: '2019'
...
---
_id: '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: '7436'
abstract:
- lang: eng
text: 'For an ordinary K3 surface over an algebraically closed field of positive
characteristic we show that every automorphism lifts to characteristic zero. Moreover,
we show that the Fourier-Mukai partners of an ordinary K3 surface are in one-to-one
correspondence with the Fourier-Mukai partners of the geometric generic fiber
of its canonical lift. We also prove that the explicit counting formula for Fourier-Mukai
partners of the K3 surfaces with Picard rank two and with discriminant equal to
minus of a prime number, in terms of the class number of the prime, holds over
a field of positive characteristic as well. We show that the image of the derived
autoequivalence group of a K3 surface of finite height in the group of isometries
of its crystalline cohomology has index at least two. Moreover, we provide a conditional
upper bound on the kernel of this natural cohomological descent map. Further,
we give an extended remark in the appendix on the possibility of an F-crystal
structure on the crystalline cohomology of a K3 surface over an algebraically
closed field of positive characteristic and show that the naive F-crystal structure
fails in being compatible with inner product. '
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tanya K
full_name: Srivastava, Tanya K
id: 4D046628-F248-11E8-B48F-1D18A9856A87
last_name: Srivastava
citation:
ama: Srivastava TK. On derived equivalences of k3 surfaces in positive characteristic.
Documenta Mathematica. 2019;24:1135-1177. doi:10.25537/dm.2019v24.1135-1177
apa: Srivastava, T. K. (2019). On derived equivalences of k3 surfaces in positive
characteristic. Documenta Mathematica. EMS Press. https://doi.org/10.25537/dm.2019v24.1135-1177
chicago: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive
Characteristic.” Documenta Mathematica. EMS Press, 2019. https://doi.org/10.25537/dm.2019v24.1135-1177.
ieee: T. K. Srivastava, “On derived equivalences of k3 surfaces in positive characteristic,”
Documenta Mathematica, vol. 24. EMS Press, pp. 1135–1177, 2019.
ista: Srivastava TK. 2019. On derived equivalences of k3 surfaces in positive characteristic.
Documenta Mathematica. 24, 1135–1177.
mla: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.”
Documenta Mathematica, vol. 24, EMS Press, 2019, pp. 1135–77, doi:10.25537/dm.2019v24.1135-1177.
short: T.K. Srivastava, Documenta Mathematica 24 (2019) 1135–1177.
date_created: 2020-02-02T23:01:06Z
date_published: 2019-05-20T00:00:00Z
date_updated: 2023-10-17T07:42:21Z
day: '20'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.25537/dm.2019v24.1135-1177
external_id:
arxiv:
- '1809.08970'
isi:
- '000517806400019'
file:
- access_level: open_access
checksum: 9a1a64bd49ab03fa4f738fb250fc4f90
content_type: application/pdf
creator: dernst
date_created: 2020-02-03T06:26:12Z
date_updated: 2020-07-14T12:47:58Z
file_id: '7438'
file_name: 2019_DocumMath_Srivastava.pdf
file_size: 469730
relation: main_file
file_date_updated: 2020-07-14T12:47:58Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1135-1177
publication: Documenta Mathematica
publication_identifier:
eissn:
- 1431-0643
issn:
- 1431-0635
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On derived equivalences of k3 surfaces in positive characteristic
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2019'
...
---
_id: '5'
abstract:
- lang: eng
text: In this paper, we introduce a quantum version of the wonderful compactification
of a group as a certain noncommutative projective scheme. Our approach stems from
the fact that the wonderful compactification encodes the asymptotics of matrix
coefficients, and from its realization as a GIT quotient of the Vinberg semigroup.
In order to define the wonderful compactification for a quantum group, we adopt
a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key
to our construction is a quantum version of the Vinberg semigroup, which we define
as a q-deformation of a certain Rees algebra, compatible with a standard Poisson
structure. Furthermore, we discuss quantum analogues of the stratification of
the wonderful compactification by orbits for a certain group action, and provide
explicit computations in the case of SL2.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Iordan V
full_name: Ganev, Iordan V
id: 447491B8-F248-11E8-B48F-1D18A9856A87
last_name: Ganev
citation:
ama: Ganev IV. The wonderful compactification for quantum groups. Journal of
the London Mathematical Society. 2019;99(3):778-806. doi:10.1112/jlms.12193
apa: Ganev, I. V. (2019). The wonderful compactification for quantum groups. Journal
of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12193
chicago: Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” Journal
of the London Mathematical Society. Wiley, 2019. https://doi.org/10.1112/jlms.12193.
ieee: I. V. Ganev, “The wonderful compactification for quantum groups,” Journal
of the London Mathematical Society, vol. 99, no. 3. Wiley, pp. 778–806, 2019.
ista: Ganev IV. 2019. The wonderful compactification for quantum groups. Journal
of the London Mathematical Society. 99(3), 778–806.
mla: Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” Journal
of the London Mathematical Society, vol. 99, no. 3, Wiley, 2019, pp. 778–806,
doi:10.1112/jlms.12193.
short: I.V. Ganev, Journal of the London Mathematical Society 99 (2019) 778–806.
date_created: 2018-12-11T11:44:06Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-09-19T10:13:08Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/jlms.12193
external_id:
isi:
- '000470025900008'
file:
- access_level: open_access
checksum: 1be56239b2cd740a0e9a084f773c22f6
content_type: application/pdf
creator: kschuh
date_created: 2020-01-07T13:31:53Z
date_updated: 2020-07-14T12:46:35Z
file_id: '7238'
file_name: 2019_Wiley_Ganev.pdf
file_size: 431754
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 99'
isi: 1
issue: '3'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 778-806
publication: Journal of the London Mathematical Society
publication_status: published
publisher: Wiley
publist_id: '8052'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The wonderful compactification for quantum groups
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 99
year: '2019'
...
---
_id: '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: '441'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikita
full_name: Kalinin, Nikita
last_name: Kalinin
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
citation:
ama: Kalinin N, Shkolnikov M. Tropical formulae for summation over a part of SL(2,Z).
European Journal of Mathematics. 2019;5(3):909–928. doi:10.1007/s40879-018-0218-0
apa: Kalinin, N., & Shkolnikov, M. (2019). Tropical formulae for summation over
a part of SL(2,Z). European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-018-0218-0
chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Tropical Formulae for Summation
over a Part of SL(2,Z).” European Journal of Mathematics. Springer Nature,
2019. https://doi.org/10.1007/s40879-018-0218-0.
ieee: N. Kalinin and M. Shkolnikov, “Tropical formulae for summation over a part
of SL(2,Z),” European Journal of Mathematics, vol. 5, no. 3. Springer Nature,
pp. 909–928, 2019.
ista: Kalinin N, Shkolnikov M. 2019. Tropical formulae for summation over a part
of SL(2,Z). European Journal of Mathematics. 5(3), 909–928.
mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Tropical Formulae for Summation over
a Part of SL(2,Z).” European Journal of Mathematics, vol. 5, no. 3, Springer
Nature, 2019, pp. 909–928, doi:10.1007/s40879-018-0218-0.
short: N. Kalinin, M. Shkolnikov, European Journal of Mathematics 5 (2019) 909–928.
date_created: 2018-12-11T11:46:29Z
date_published: 2019-09-15T00:00:00Z
date_updated: 2021-01-12T07:56:46Z
day: '15'
department:
- _id: TaHa
doi: 10.1007/s40879-018-0218-0
ec_funded: 1
external_id:
arxiv:
- '1711.02089'
intvolume: ' 5'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1711.02089
month: '09'
oa: 1
oa_version: Preprint
page: 909–928
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
publist_id: '7382'
quality_controlled: '1'
scopus_import: 1
status: public
title: Tropical formulae for summation over a part of SL(2,Z)
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 5
year: '2019'
...
---
_id: '303'
abstract:
- lang: eng
text: The theory of tropical series, that we develop here, firstly appeared in the
study of the growth of pluriharmonic functions. Motivated by waves in sandpile
models we introduce a dynamic on the set of tropical series, and it is experimentally
observed that this dynamic obeys a power law. So, this paper serves as a compilation
of results we need for other articles and also introduces several objects interesting
by themselves.
acknowledgement: The first author, Nikita Kalinin, is funded by SNCF PostDoc.Mobility
grant 168647. Support from the Basic Research Program of the National Research University
Higher School of Economics is gratefully acknowledged. The second author, Mikhail
Shkolnikov, is supported in part by the grant 159240 of the Swiss National Science
Foundation as well as by the National Center of Competence in Research SwissMAP
of the Swiss National Science Foundation.
article_processing_charge: No
arxiv: 1
author:
- first_name: Nikita
full_name: Kalinin, Nikita
last_name: Kalinin
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
citation:
ama: Kalinin N, Shkolnikov M. Introduction to tropical series and wave dynamic on
them. Discrete and Continuous Dynamical Systems- Series A. 2018;38(6):2827-2849.
doi:10.3934/dcds.2018120
apa: Kalinin, N., & Shkolnikov, M. (2018). Introduction to tropical series and
wave dynamic on them. Discrete and Continuous Dynamical Systems- Series A.
AIMS. https://doi.org/10.3934/dcds.2018120
chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series
and Wave Dynamic on Them.” Discrete and Continuous Dynamical Systems- Series
A. AIMS, 2018. https://doi.org/10.3934/dcds.2018120.
ieee: N. Kalinin and M. Shkolnikov, “Introduction to tropical series and wave dynamic
on them,” Discrete and Continuous Dynamical Systems- Series A, vol. 38,
no. 6. AIMS, pp. 2827–2849, 2018.
ista: Kalinin N, Shkolnikov M. 2018. Introduction to tropical series and wave dynamic
on them. Discrete and Continuous Dynamical Systems- Series A. 38(6), 2827–2849.
mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and
Wave Dynamic on Them.” Discrete and Continuous Dynamical Systems- Series A,
vol. 38, no. 6, AIMS, 2018, pp. 2827–49, doi:10.3934/dcds.2018120.
short: N. Kalinin, M. Shkolnikov, Discrete and Continuous Dynamical Systems- Series
A 38 (2018) 2827–2849.
date_created: 2018-12-11T11:45:43Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-12T07:45:37Z
day: '01'
department:
- _id: TaHa
doi: 10.3934/dcds.2018120
external_id:
arxiv:
- '1706.03062'
isi:
- '000438818400007'
intvolume: ' 38'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.03062
month: '06'
oa: 1
oa_version: Submitted Version
page: 2827 - 2849
publication: Discrete and Continuous Dynamical Systems- Series A
publication_status: published
publisher: AIMS
publist_id: '7576'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Introduction to tropical series and wave dynamic on them
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 38
year: '2018'
...
---
_id: '322'
abstract:
- lang: eng
text: We construct quantizations of multiplicative hypertoric varieties using an
algebra of q-difference operators on affine space, where q is a root of unity
in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the
multiplicative hypertoric variety and admits an explicit finite étale splitting.
The global sections of this Azumaya algebra is a hypertoric quantum group, and
we prove a localization theorem. We introduce a general framework of Frobenius
quantum moment maps and their Hamiltonian reductions; our results shed light on
an instance of this framework.
acknowledgement: "National Science Foundation: Graduate Research Fellowship and grant
No.0932078000; ERC Advanced Grant “Arithmetic and Physics of Higgs moduli spaces”
No. 320593 \r\nThe author is grateful to David Jordan for suggesting this project
and providing guidance throughout, particularly for the formulation of Frobenius
quantum moment maps and key ideas in the proofs of Theorems 3.12 and 4.8. Special
thanks to David Ben-Zvi (the author's PhD advisor) for numerous discussions and
constant encouragement, and for suggesting the term ‘hypertoric quantum group.’
Many results appearing in the current paper were proven independently by Nicholas
Cooney; the author is grateful to Nicholas for sharing his insight on various topics,
including Proposition 3.8. The author also thanks Nicholas Proudfoot for relating
the definition of multiplicative hypertoric varieties, as well as the content of
Remark 2.14. The author also benefited immensely from the close reading and detailed
comments of an anonymous referee, and from conversations with Justin Hilburn, Kobi
Kremnitzer, Michael McBreen, Tom Nevins, Travis Schedler, and Ben Webster. \r\n\r\n\r\n\r\n"
article_processing_charge: No
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: '5999'
abstract:
- lang: eng
text: "We introduce for each quiver Q and each algebraic oriented cohomology theory
A, the cohomological Hall algebra (CoHA) of Q, as the A-homology of the moduli
of representations of the preprojective algebra of Q. This generalizes the K-theoretic
Hall algebra of commuting varieties defined by Schiffmann-Vasserot. When A is
the Morava K-theory, we show evidence that this algebra is a candidate for Lusztig's
reformulated conjecture on modular representations of algebraic groups.\r\nWe
construct an action of the preprojective CoHA on the A-homology of Nakajima quiver
varieties. We compare this with the action of the Borel subalgebra of Yangian
when A is the intersection theory. We also give a shuffle algebra description
of this CoHA in terms of the underlying formal group law of A. As applications,
we obtain a shuffle description of the Yangian. "
article_processing_charge: No
arxiv: 1
author:
- first_name: Yaping
full_name: Yang, Yaping
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra.
Proceedings of the London Mathematical Society. 2018;116(5):1029-1074.
doi:10.1112/plms.12111
apa: Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective
algebra. Proceedings of the London Mathematical Society. Oxford University
Press. https://doi.org/10.1112/plms.12111
chicago: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective
Algebra.” Proceedings of the London Mathematical Society. Oxford University
Press, 2018. https://doi.org/10.1112/plms.12111.
ieee: Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,”
Proceedings of the London Mathematical Society, vol. 116, no. 5. Oxford
University Press, pp. 1029–1074, 2018.
ista: Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra.
Proceedings of the London Mathematical Society. 116(5), 1029–1074.
mla: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective
Algebra.” Proceedings of the London Mathematical Society, vol. 116, no.
5, Oxford University Press, 2018, pp. 1029–74, doi:10.1112/plms.12111.
short: Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018)
1029–1074.
date_created: 2019-02-14T13:14:22Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2023-09-19T14:37:19Z
day: '01'
department:
- _id: TaHa
doi: 10.1112/plms.12111
external_id:
arxiv:
- '1407.7994'
isi:
- '000431506400001'
intvolume: ' 116'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1407.7994
month: '05'
oa: 1
oa_version: Preprint
page: 1029-1074
publication: Proceedings of the London Mathematical Society
publication_identifier:
issn:
- 0024-6115
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The cohomological Hall algebra of a preprojective algebra
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 116
year: '2018'
...
---
_id: '61'
abstract:
- lang: eng
text: 'We prove that there is no strongly regular graph (SRG) with parameters (460;
153; 32; 60). The proof is based on a recent lower bound on the number of 4-cliques
in a SRG and some applications of Euclidean representation of SRGs. '
article_processing_charge: No
arxiv: 1
author:
- first_name: Andriy
full_name: Bondarenko, Andriy
last_name: Bondarenko
- first_name: Anton
full_name: Mellit, Anton
id: 388D3134-F248-11E8-B48F-1D18A9856A87
last_name: Mellit
- first_name: Andriy
full_name: Prymak, Andriy
last_name: Prymak
- first_name: Danylo
full_name: Radchenko, Danylo
last_name: Radchenko
- first_name: Maryna
full_name: Viazovska, Maryna
last_name: Viazovska
citation:
ama: 'Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. There is no strongly
regular graph with parameters (460; 153; 32; 60). In: Contemporary Computational
Mathematics. Springer; 2018:131-134. doi:10.1007/978-3-319-72456-0_7'
apa: Bondarenko, A., Mellit, A., Prymak, A., Radchenko, D., & Viazovska, M.
(2018). There is no strongly regular graph with parameters (460; 153; 32; 60).
In Contemporary Computational Mathematics (pp. 131–134). Springer. https://doi.org/10.1007/978-3-319-72456-0_7
chicago: Bondarenko, Andriy, Anton Mellit, Andriy Prymak, Danylo Radchenko, and
Maryna Viazovska. “There Is No Strongly Regular Graph with Parameters (460; 153;
32; 60).” In Contemporary Computational Mathematics, 131–34. Springer,
2018. https://doi.org/10.1007/978-3-319-72456-0_7.
ieee: A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, and M. Viazovska, “There
is no strongly regular graph with parameters (460; 153; 32; 60),” in Contemporary
Computational Mathematics, Springer, 2018, pp. 131–134.
ista: 'Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. 2018.There is
no strongly regular graph with parameters (460; 153; 32; 60). In: Contemporary
Computational Mathematics. , 131–134.'
mla: Bondarenko, Andriy, et al. “There Is No Strongly Regular Graph with Parameters
(460; 153; 32; 60).” Contemporary Computational Mathematics, Springer,
2018, pp. 131–34, doi:10.1007/978-3-319-72456-0_7.
short: A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, M. Viazovska, in:, Contemporary
Computational Mathematics, Springer, 2018, pp. 131–134.
date_created: 2018-12-11T11:44:25Z
date_published: 2018-05-23T00:00:00Z
date_updated: 2021-01-12T08:06:06Z
day: '23'
department:
- _id: TaHa
doi: 10.1007/978-3-319-72456-0_7
extern: '1'
external_id:
arxiv:
- '1509.06286'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1509.06286
month: '05'
oa: 1
oa_version: Preprint
page: 131 - 134
publication: Contemporary Computational Mathematics
publication_status: published
publisher: Springer
publist_id: '7993'
quality_controlled: '1'
status: public
title: There is no strongly regular graph with parameters (460; 153; 32; 60)
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '64'
abstract:
- lang: eng
text: Tropical geometry, an established field in pure mathematics, is a place where
string theory, mirror symmetry, computational algebra, auction theory, and so
forth meet and influence one another. In this paper, we report on our discovery
of a tropical model with self-organized criticality (SOC) behavior. Our model
is continuous, in contrast to all known models of SOC, and is a certain scaling
limit of the sandpile model, the first and archetypical model of SOC. We describe
how our model is related to pattern formation and proportional growth phenomena
and discuss the dichotomy between continuous and discrete models in several contexts.
Our aim in this context is to present an idealized tropical toy model (cf. Turing
reaction-diffusion model), requiring further investigation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikita
full_name: Kalinin, Nikita
last_name: Kalinin
- first_name: Aldo
full_name: Guzmán Sáenz, Aldo
last_name: Guzmán Sáenz
- first_name: Y
full_name: Prieto, Y
last_name: Prieto
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
- first_name: V
full_name: Kalinina, V
last_name: Kalinina
- first_name: Ernesto
full_name: Lupercio, Ernesto
last_name: Lupercio
citation:
ama: 'Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E.
Self-organized criticality and pattern emergence through the lens of tropical
geometry. PNAS: Proceedings of the National Academy of Sciences of the United
States of America. 2018;115(35):E8135-E8142. doi:10.1073/pnas.1805847115'
apa: 'Kalinin, N., Guzmán Sáenz, A., Prieto, Y., Shkolnikov, M., Kalinina, V., &
Lupercio, E. (2018). Self-organized criticality and pattern emergence through
the lens of tropical geometry. PNAS: Proceedings of the National Academy of
Sciences of the United States of America. National Academy of Sciences. https://doi.org/10.1073/pnas.1805847115'
chicago: 'Kalinin, Nikita, Aldo Guzmán Sáenz, Y Prieto, Mikhail Shkolnikov, V Kalinina,
and Ernesto Lupercio. “Self-Organized Criticality and Pattern Emergence through
the Lens of Tropical Geometry.” PNAS: Proceedings of the National Academy of
Sciences of the United States of America. National Academy of Sciences, 2018.
https://doi.org/10.1073/pnas.1805847115.'
ieee: 'N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, and E.
Lupercio, “Self-organized criticality and pattern emergence through the lens of
tropical geometry,” PNAS: Proceedings of the National Academy of Sciences of
the United States of America, vol. 115, no. 35. National Academy of Sciences,
pp. E8135–E8142, 2018.'
ista: 'Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E.
2018. Self-organized criticality and pattern emergence through the lens of tropical
geometry. PNAS: Proceedings of the National Academy of Sciences of the United
States of America. 115(35), E8135–E8142.'
mla: 'Kalinin, Nikita, et al. “Self-Organized Criticality and Pattern Emergence
through the Lens of Tropical Geometry.” PNAS: Proceedings of the National Academy
of Sciences of the United States of America, vol. 115, no. 35, National Academy
of Sciences, 2018, pp. E8135–42, doi:10.1073/pnas.1805847115.'
short: 'N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, E. Lupercio,
PNAS: Proceedings of the National Academy of Sciences of the United States of
America 115 (2018) E8135–E8142.'
date_created: 2018-12-11T11:44:26Z
date_published: 2018-08-28T00:00:00Z
date_updated: 2023-09-18T08:41:16Z
day: '28'
department:
- _id: TaHa
doi: 10.1073/pnas.1805847115
ec_funded: 1
external_id:
arxiv:
- '1806.09153'
isi:
- '000442861600009'
intvolume: ' 115'
isi: 1
issue: '35'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1806.09153
month: '08'
oa: 1
oa_version: Preprint
page: E8135 - E8142
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: 'PNAS: Proceedings of the National Academy of Sciences of the United
States of America'
publication_identifier:
issn:
- '00278424'
publication_status: published
publisher: National Academy of Sciences
publist_id: '7990'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Self-organized criticality and pattern emergence through the lens of tropical
geometry
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 115
year: '2018'
...
---
_id: '6525'
abstract:
- lang: eng
text: This chapter finds an agreement of equivariant indices of semi-classical homomorphisms
between pairwise mirror branes in the GL2 Higgs moduli space on a Riemann surface.
On one side of the agreement, components of the Lagrangian brane of U(1,1) Higgs
bundles, whose mirror was proposed by Hitchin to be certain even exterior powers
of the hyperholomorphic Dirac bundle on the SL2 Higgs moduli space, are present.
The agreement arises from a mysterious functional equation. This gives strong
computational evidence for Hitchin’s proposal.
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Anton
full_name: Mellit, Anton
id: 388D3134-F248-11E8-B48F-1D18A9856A87
last_name: Mellit
- first_name: Du
full_name: Pei, Du
last_name: Pei
citation:
ama: 'Hausel T, Mellit A, Pei D. Mirror symmetry with branes by equivariant verlinde
formulas. In: Geometry and Physics: Volume I. Oxford University Press;
2018:189-218. doi:10.1093/oso/9780198802013.003.0009'
apa: 'Hausel, T., Mellit, A., & Pei, D. (2018). Mirror symmetry with branes
by equivariant verlinde formulas. In Geometry and Physics: Volume I (pp.
189–218). Oxford University Press. https://doi.org/10.1093/oso/9780198802013.003.0009'
chicago: 'Hausel, Tamás, Anton Mellit, and Du Pei. “Mirror Symmetry with Branes
by Equivariant Verlinde Formulas.” In Geometry and Physics: Volume I, 189–218.
Oxford University Press, 2018. https://doi.org/10.1093/oso/9780198802013.003.0009.'
ieee: 'T. Hausel, A. Mellit, and D. Pei, “Mirror symmetry with branes by equivariant
verlinde formulas,” in Geometry and Physics: Volume I, Oxford University
Press, 2018, pp. 189–218.'
ista: 'Hausel T, Mellit A, Pei D. 2018.Mirror symmetry with branes by equivariant
verlinde formulas. In: Geometry and Physics: Volume I. , 189–218.'
mla: 'Hausel, Tamás, et al. “Mirror Symmetry with Branes by Equivariant Verlinde
Formulas.” Geometry and Physics: Volume I, Oxford University Press, 2018,
pp. 189–218, doi:10.1093/oso/9780198802013.003.0009.'
short: 'T. Hausel, A. Mellit, D. Pei, in:, Geometry and Physics: Volume I, Oxford
University Press, 2018, pp. 189–218.'
date_created: 2019-06-06T12:42:01Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2021-01-12T08:07:52Z
day: '01'
department:
- _id: TaHa
doi: 10.1093/oso/9780198802013.003.0009
language:
- iso: eng
month: '01'
oa_version: None
page: 189-218
publication: 'Geometry and Physics: Volume I'
publication_identifier:
isbn:
- '9780198802013'
- '9780191840500'
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: 1
status: public
title: Mirror symmetry with branes by equivariant verlinde formulas
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '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'
...