---
_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: '10024'
abstract:
- lang: eng
text: In this paper, we introduce a random environment for the exclusion process
in obtained by assigning a maximal occupancy to each site. This maximal occupancy
is allowed to randomly vary among sites, and partial exclusion occurs. Under the
assumption of ergodicity under translation and uniform ellipticity of the environment,
we derive a quenched hydrodynamic limit in path space by strengthening the mild
solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose,
we prove, employing the technology developed for the random conductance model,
a homogenization result in the form of an arbitrary starting point quenched invariance
principle for a single particle in the same environment, which is a result of
independent interest. The self-duality property of the partial exclusion process
allows us to transfer this homogenization result to the particle system and, then,
apply the tightness criterion in Redig et al. (2020).
acknowledgement: The authors would like to thank Marek Biskup and Alberto Chiarini
for useful suggestions and Cristian Giardina, Frank den Hollander and Shubhamoy Nandan for inspiring discussions. S.F. acknowledges Simona Villa for her help in creating the picture. Furthermore,
the authors thank two anonymous referees for the careful reading of the manuscript. S.F.
acknowledges financial support from NWO, The Netherlands via the grant TOP1.17.019.
F.S. acknowledges financial support from NWO via the TOP1 grant 613.001.552 as well as
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie-Skłodowska-Curie grant agreement No. 754411.
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Simone
full_name: Floreani, Simone
last_name: Floreani
- first_name: Frank
full_name: Redig, Frank
last_name: Redig
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process
in random environment. Stochastic Processes and their Applications. 2021;142:124-158.
doi:10.1016/j.spa.2021.08.006
apa: Floreani, S., Redig, F., & Sau, F. (2021). Hydrodynamics for the partial
exclusion process in random environment. Stochastic Processes and Their Applications.
Elsevier. https://doi.org/10.1016/j.spa.2021.08.006
chicago: Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the
Partial Exclusion Process in Random Environment.” Stochastic Processes and
Their Applications. Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006.
ieee: S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion
process in random environment,” Stochastic Processes and their Applications,
vol. 142. Elsevier, pp. 124–158, 2021.
ista: Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion
process in random environment. Stochastic Processes and their Applications. 142,
124–158.
mla: Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in
Random Environment.” Stochastic Processes and Their Applications, vol.
142, Elsevier, 2021, pp. 124–58, doi:10.1016/j.spa.2021.08.006.
short: S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications
142 (2021) 124–158.
date_created: 2021-09-19T22:01:25Z
date_published: 2021-08-27T00:00:00Z
date_updated: 2023-08-14T06:52:43Z
day: '27'
ddc:
- '519'
department:
- _id: JaMa
doi: 10.1016/j.spa.2021.08.006
ec_funded: 1
external_id:
arxiv:
- '1911.12564'
isi:
- '000697748500005'
file:
- access_level: open_access
checksum: 56768c553d7218ee5714902ffec90ec4
content_type: application/pdf
creator: dernst
date_created: 2022-05-13T07:55:50Z
date_updated: 2022-05-13T07:55:50Z
file_id: '11370'
file_name: 2021_StochasticProcessesAppl_Floreani.pdf
file_size: 2115791
relation: main_file
success: 1
file_date_updated: 2022-05-13T07:55:50Z
has_accepted_license: '1'
intvolume: ' 142'
isi: 1
keyword:
- hydrodynamic limit
- random environment
- random conductance model
- arbitrary starting point quenched invariance principle
- duality
- mild solution
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 124-158
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Stochastic Processes and their Applications
publication_identifier:
issn:
- 0304-4149
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hydrodynamics for the partial exclusion process in random environment
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: 142
year: '2021'
...
---
_id: '10033'
abstract:
- lang: eng
text: The ⊗*-monoidal structure on the category of sheaves on the Ran space is not
pro-nilpotent in the sense of [3]. However, under some connectivity assumptions,
we prove that Koszul duality induces an equivalence of categories and that this
equivalence behaves nicely with respect to Verdier duality on the Ran space and
integrating along the Ran space, i.e. taking factorization homology. Based on
ideas sketched in [4], we show that these results also offer a simpler alternative
to one of the two main steps in the proof of the Atiyah-Bott formula given in
[7] and [5].
acknowledgement: 'The author would like to express his gratitude to D. Gaitsgory,
without whose tireless guidance and encouragement in pursuing this problem, this
work would not have been possible. The author is grateful to his advisor B.C. Ngô
for many years of patient guidance and support. This paper is revised while the
author is a postdoc in Hausel group at IST Austria. We thank him and the group for
providing a wonderful research environment. The author also gratefully acknowledges
the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization
Homology,” Austrian Science Fund (FWF): M 2751.'
article_number: '107992'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Quoc P
full_name: Ho, Quoc P
id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
last_name: Ho
orcid: 0000-0001-6889-1418
citation:
ama: Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances
in Mathematics. 2021;392. doi:10.1016/j.aim.2021.107992
apa: Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul
duality. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107992
chicago: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul
Duality.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107992.
ieee: Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,”
Advances in Mathematics, vol. 392. Elsevier, 2021.
ista: Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality.
Advances in Mathematics. 392, 107992.
mla: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.”
Advances in Mathematics, vol. 392, 107992, Elsevier, 2021, doi:10.1016/j.aim.2021.107992.
short: Q.P. Ho, Advances in Mathematics 392 (2021).
date_created: 2021-09-21T15:58:59Z
date_published: 2021-09-21T00:00:00Z
date_updated: 2023-08-14T06:54:35Z
day: '21'
ddc:
- '514'
department:
- _id: TaHa
doi: 10.1016/j.aim.2021.107992
external_id:
arxiv:
- '1610.00212'
isi:
- '000707040300031'
file:
- access_level: open_access
checksum: f3c0086d41af11db31c00014efb38072
content_type: application/pdf
creator: qho
date_created: 2021-09-21T15:58:52Z
date_updated: 2021-09-21T15:58:52Z
file_id: '10034'
file_name: 1-s2.0-S000187082100431X-main.pdf
file_size: 840635
relation: main_file
file_date_updated: 2021-09-21T15:58:52Z
has_accepted_license: '1'
intvolume: ' 392'
isi: 1
keyword:
- Chiral algebras
- Chiral homology
- Factorization algebras
- Koszul duality
- Ran space
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 26B96266-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02751
name: Algebro-Geometric Applications of Factorization Homology
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: The Atiyah-Bott formula and connectivity in chiral Koszul duality
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: 392
year: '2021'
...
---
_id: '10613'
abstract:
- lang: eng
text: Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci,
and Redig, we first provide a general framework for the study of scaling limits
of higher-order fields. Then, by considering the same class of infinite interacting
particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion
and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic
limit, and convergence for the equilibrium fluctuations, of higher-order fields.
In particular, the limit fields exhibit a tensor structure. Our fluctuation result
differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional
Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium
fluctuations, of higher-order fields. In particular, the limit fields exhibit
a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}],
since we consider a different notion of higher-order fluctuation fields.
acknowledgement: "F.S. would like to thank Mario Ayala and Frank Redig for useful
discussions. J.P.C. acknowledges partial financial support from the US National
Science Foundation (DMS-1855604). F.S. was financially supported by the European
Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie
grant agreement No. 754411.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Joe P.
full_name: Chen, Joe P.
last_name: Chen
- first_name: Federico
full_name: Sau, Federico
id: E1836206-9F16-11E9-8814-AEFDE5697425
last_name: Sau
citation:
ama: Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of
interacting particle systems. Markov Processes And Related Fields. 2021;27(3):339-380.
apa: Chen, J. P., & Sau, F. (2021). Higher-order hydrodynamics and equilibrium
fluctuations of interacting particle systems. Markov Processes And Related
Fields. Polymat Publishing.
chicago: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
Fluctuations of Interacting Particle Systems.” Markov Processes And Related
Fields. Polymat Publishing, 2021.
ieee: J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations
of interacting particle systems,” Markov Processes And Related Fields,
vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.
ista: Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations
of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380.
mla: Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium
Fluctuations of Interacting Particle Systems.” Markov Processes And Related
Fields, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80.
short: J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380.
date_created: 2022-01-10T14:02:31Z
date_published: 2021-03-16T00:00:00Z
date_updated: 2022-01-10T15:29:08Z
day: '16'
department:
- _id: JaMa
ec_funded: 1
external_id:
arxiv:
- '2008.13403'
intvolume: ' 27'
issue: '3'
keyword:
- interacting particle systems
- higher-order fields
- hydrodynamic limit
- equilibrium fluctuations
- duality
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2008.13403
month: '03'
oa: 1
oa_version: Preprint
page: 339-380
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Markov Processes And Related Fields
publication_identifier:
issn:
- 1024-2953
publication_status: published
publisher: Polymat Publishing
quality_controlled: '1'
related_material:
link:
- description: Link to Abstract on publisher's website
relation: other
url: http://math-mprf.org/journal/articles/id1614/
- description: Referred to in Abstract
relation: used_for_analysis_in
url: https://arxiv.org/abs/2004.08412
status: public
title: Higher-order hydrodynamics and equilibrium fluctuations of interacting particle
systems
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 27
year: '2021'
...