---
_id: '14499'
abstract:
- lang: eng
text: "An n-vertex graph is called C-Ramsey if it has no clique or independent set
of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper,
we study edge statistics in Ramsey graphs, in particular obtaining very precise
control of the distribution of the number of edges in a random vertex subset of
a C-Ramsey graph. This brings together two ongoing lines of research: the study
of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability
for low-degree polynomials of independent random variables.\r\n\r\nThe proof proceeds
via an ‘additive structure’ dichotomy on the degree sequence and involves a wide
range of different tools from Fourier analysis, random matrix theory, the theory
of Boolean functions, probabilistic combinatorics and low-rank approximation.
In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright
theorem on small-ball probability for polynomials of Gaussians, which we believe
is of independent interest. One of the consequences of our result is the resolution
of an old conjecture of Erdős and McKay, for which Erdős reiterated in several
of his open problem collections and for which he offered one of his notorious
monetary prizes."
acknowledgement: Kwan was supported for part of this work by ERC Starting Grant ‘RANDSTRUCT’
No. 101076777. Sah and Sawhney were supported by NSF Graduate Research Fellowship
Program DGE-2141064. Sah was supported by the PD Soros Fellowship. Sauermann was
supported by NSF Award DMS-2100157, and for part of this work by a Sloan Research
Fellowship.
article_number: e21
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Matthew Alan
full_name: Kwan, Matthew Alan
id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
last_name: Kwan
orcid: 0000-0002-4003-7567
- first_name: Ashwin
full_name: Sah, Ashwin
last_name: Sah
- first_name: Lisa
full_name: Sauermann, Lisa
last_name: Sauermann
- first_name: Mehtaab
full_name: Sawhney, Mehtaab
last_name: Sawhney
citation:
ama: Kwan MA, Sah A, Sauermann L, Sawhney M. Anticoncentration in Ramsey graphs
and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 2023;11.
doi:10.1017/fmp.2023.17
apa: Kwan, M. A., Sah, A., Sauermann, L., & Sawhney, M. (2023). Anticoncentration
in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics,
Pi. Cambridge University Press. https://doi.org/10.1017/fmp.2023.17
chicago: Kwan, Matthew Alan, Ashwin Sah, Lisa Sauermann, and Mehtaab Sawhney. “Anticoncentration
in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” Forum of Mathematics,
Pi. Cambridge University Press, 2023. https://doi.org/10.1017/fmp.2023.17.
ieee: M. A. Kwan, A. Sah, L. Sauermann, and M. Sawhney, “Anticoncentration in Ramsey
graphs and a proof of the Erdős–McKay conjecture,” Forum of Mathematics, Pi,
vol. 11. Cambridge University Press, 2023.
ista: Kwan MA, Sah A, Sauermann L, Sawhney M. 2023. Anticoncentration in Ramsey
graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 11,
e21.
mla: Kwan, Matthew Alan, et al. “Anticoncentration in Ramsey Graphs and a Proof
of the Erdős–McKay Conjecture.” Forum of Mathematics, Pi, vol. 11, e21,
Cambridge University Press, 2023, doi:10.1017/fmp.2023.17.
short: M.A. Kwan, A. Sah, L. Sauermann, M. Sawhney, Forum of Mathematics, Pi 11
(2023).
date_created: 2023-11-07T09:02:48Z
date_published: 2023-08-24T00:00:00Z
date_updated: 2023-11-07T09:18:57Z
day: '24'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.1017/fmp.2023.17
external_id:
arxiv:
- '2208.02874'
file:
- access_level: open_access
checksum: 54b824098d59073cc87a308d458b0a3e
content_type: application/pdf
creator: dernst
date_created: 2023-11-07T09:16:23Z
date_updated: 2023-11-07T09:16:23Z
file_id: '14500'
file_name: 2023_ForumMathematics_Kwan.pdf
file_size: 1218719
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success: 1
file_date_updated: 2023-11-07T09:16:23Z
has_accepted_license: '1'
intvolume: ' 11'
keyword:
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Mathematical Physics
- Statistics and Probability
- Algebra and Number Theory
- Analysis
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: bd95085b-d553-11ed-ba76-e55d3349be45
grant_number: '101076777'
name: Randomness and structure in combinatorics
publication: Forum of Mathematics, Pi
publication_identifier:
issn:
- 2050-5086
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...
---
_id: '14756'
abstract:
- lang: eng
text: "We prove the r-spin cobordism hypothesis in the setting of (weak) 2-categories
for every positive integer r: the 2-groupoid of 2-dimensional fully extended r-spin
TQFTs with given target is equivalent to the homotopy fixed points of an induced
Spin 2r -action. In particular, such TQFTs are classified by fully dualisable
objects together with a trivialisation of the rth power of their Serre automorphisms.
For r=1, we recover the oriented case (on which our proof builds), while ordinary
spin structures correspond to r=2.\r\nTo construct examples, we explicitly describe
Spin 2r-homotopy fixed points in the equivariant completion of any symmetric
monoidal 2-category. We also show that every object in a 2-category of Landau–Ginzburg
models gives rise to fully extended spin TQFTs and that half of these do not factor
through the oriented bordism 2-category."
acknowledgement: "N.C. is supported by the DFG Heisenberg Programme.\r\nWe are grateful
to Tobias Dyckerhoff, Lukas Müller, Ingo Runkel, and Christopher Schommer-Pries
for helpful discussions."
article_processing_charge: Yes
article_type: original
author:
- first_name: Nils
full_name: Carqueville, Nils
last_name: Carqueville
- first_name: Lorant
full_name: Szegedy, Lorant
id: 7943226E-220E-11EA-94C7-D59F3DDC885E
last_name: Szegedy
orcid: 0000-0003-2834-5054
citation:
ama: Carqueville N, Szegedy L. Fully extended r-spin TQFTs. Quantum Topology.
2023;14(3):467-532. doi:10.4171/qt/193
apa: Carqueville, N., & Szegedy, L. (2023). Fully extended r-spin TQFTs. Quantum
Topology. European Mathematical Society. https://doi.org/10.4171/qt/193
chicago: Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” Quantum
Topology. European Mathematical Society, 2023. https://doi.org/10.4171/qt/193.
ieee: N. Carqueville and L. Szegedy, “Fully extended r-spin TQFTs,” Quantum Topology,
vol. 14, no. 3. European Mathematical Society, pp. 467–532, 2023.
ista: Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology.
14(3), 467–532.
mla: Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” Quantum
Topology, vol. 14, no. 3, European Mathematical Society, 2023, pp. 467–532,
doi:10.4171/qt/193.
short: N. Carqueville, L. Szegedy, Quantum Topology 14 (2023) 467–532.
date_created: 2024-01-08T13:14:48Z
date_published: 2023-10-16T00:00:00Z
date_updated: 2024-01-09T09:27:46Z
day: '16'
ddc:
- '530'
department:
- _id: MiLe
doi: 10.4171/qt/193
file:
- access_level: open_access
checksum: b0590aff6e7ec89cc149ba94d459d3a3
content_type: application/pdf
creator: dernst
date_created: 2024-01-09T09:25:34Z
date_updated: 2024-01-09T09:25:34Z
file_id: '14764'
file_name: 2023_QuantumTopol_Carqueville.pdf
file_size: 707344
relation: main_file
success: 1
file_date_updated: 2024-01-09T09:25:34Z
has_accepted_license: '1'
intvolume: ' 14'
issue: '3'
keyword:
- Geometry and Topology
- Mathematical Physics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 467-532
publication: Quantum Topology
publication_identifier:
issn:
- 1663-487X
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fully extended r-spin TQFTs
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: 14
year: '2023'
...
---
_id: '14192'
abstract:
- lang: eng
text: For the Fröhlich model of the large polaron, we prove that the ground state
energy as a function of the total momentum has a unique global minimum at momentum
zero. This implies the non-existence of a ground state of the translation invariant
Fröhlich Hamiltonian and thus excludes the possibility of a localization transition
at finite coupling.
acknowledgement: D.M. and K.M. thank Robert Seiringer for helpful discussions. Open
access funding provided by Institute of Science and Technology (IST Austria). Financial
support from the Agence Nationale de la Recherche (ANR) through the projects ANR-17-CE40-0016,
ANR-17-CE40-0007-01, ANR-17-EURE-0002 (J.L.) and from the European Union’s Horizon
2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement
No. 665386 (K.M.) is gratefully acknowledged.
article_number: '17'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jonas
full_name: Lampart, Jonas
last_name: Lampart
- first_name: David Johannes
full_name: Mitrouskas, David Johannes
id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
last_name: Mitrouskas
- first_name: Krzysztof
full_name: Mysliwy, Krzysztof
id: 316457FC-F248-11E8-B48F-1D18A9856A87
last_name: Mysliwy
citation:
ama: Lampart J, Mitrouskas DJ, Mysliwy K. On the global minimum of the energy–momentum
relation for the polaron. Mathematical Physics, Analysis and Geometry.
2023;26(3). doi:10.1007/s11040-023-09460-x
apa: Lampart, J., Mitrouskas, D. J., & Mysliwy, K. (2023). On the global minimum
of the energy–momentum relation for the polaron. Mathematical Physics, Analysis
and Geometry. Springer Nature. https://doi.org/10.1007/s11040-023-09460-x
chicago: Lampart, Jonas, David Johannes Mitrouskas, and Krzysztof Mysliwy. “On the
Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical
Physics, Analysis and Geometry. Springer Nature, 2023. https://doi.org/10.1007/s11040-023-09460-x.
ieee: J. Lampart, D. J. Mitrouskas, and K. Mysliwy, “On the global minimum of the
energy–momentum relation for the polaron,” Mathematical Physics, Analysis and
Geometry, vol. 26, no. 3. Springer Nature, 2023.
ista: Lampart J, Mitrouskas DJ, Mysliwy K. 2023. On the global minimum of the energy–momentum
relation for the polaron. Mathematical Physics, Analysis and Geometry. 26(3),
17.
mla: Lampart, Jonas, et al. “On the Global Minimum of the Energy–Momentum Relation
for the Polaron.” Mathematical Physics, Analysis and Geometry, vol. 26,
no. 3, 17, Springer Nature, 2023, doi:10.1007/s11040-023-09460-x.
short: J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and
Geometry 26 (2023).
date_created: 2023-08-22T14:09:47Z
date_published: 2023-07-26T00:00:00Z
date_updated: 2023-12-13T12:16:19Z
day: '26'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11040-023-09460-x
external_id:
arxiv:
- '2206.14708'
isi:
- '001032992600001'
file:
- access_level: open_access
checksum: f0941cc66cb3ed06a12ca4b7e356cfd6
content_type: application/pdf
creator: dernst
date_created: 2023-08-23T10:59:15Z
date_updated: 2023-08-23T10:59:15Z
file_id: '14225'
file_name: 2023_MathPhysics_Lampart.pdf
file_size: 317026
relation: main_file
success: 1
file_date_updated: 2023-08-23T10:59:15Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
issue: '3'
keyword:
- Geometry and Topology
- Mathematical Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
eissn:
- 1572-9656
issn:
- 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the global minimum of the energy–momentum relation for the polaron
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: 26
year: '2023'
...
---
_id: '12287'
abstract:
- lang: eng
text: We present criteria for establishing a triangulation of a manifold. Given
a manifold M, a simplicial complex A, and a map H from the underlying space of
A to M, our criteria are presented in local coordinate charts for M, and ensure
that H is a homeomorphism. These criteria do not require a differentiable structure,
or even an explicit metric on M. No Delaunay property of A is assumed. The result
provides a triangulation guarantee for algorithms that construct a simplicial
complex by working in local coordinate patches. Because the criteria are easily
verified in such a setting, they are expected to be of general use.
acknowledgement: "This work has been funded by the European Research Council under
the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations
of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan
Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh
was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by
the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken
also received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian
Science Fund (FWF): M-3073. A part of the results described in this paper were presented
at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science
Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- first_name: Ramsay
full_name: Dyer, Ramsay
last_name: Dyer
- first_name: Arijit
full_name: Ghosh, Arijit
last_name: Ghosh
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating
general manifolds. Discrete & Computational Geometry. 2023;69:156-191.
doi:10.1007/s00454-022-00431-7
apa: Boissonnat, J.-D., Dyer, R., Ghosh, A., & Wintraecken, M. (2023). Local
criteria for triangulating general manifolds. Discrete & Computational
Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00431-7
chicago: Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken.
“Local Criteria for Triangulating General Manifolds.” Discrete & Computational
Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00431-7.
ieee: J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for
triangulating general manifolds,” Discrete & Computational Geometry,
vol. 69. Springer Nature, pp. 156–191, 2023.
ista: Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating
general manifolds. Discrete & Computational Geometry. 69, 156–191.
mla: Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.”
Discrete & Computational Geometry, vol. 69, Springer Nature, 2023,
pp. 156–91, doi:10.1007/s00454-022-00431-7.
short: J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete & Computational
Geometry 69 (2023) 156–191.
date_created: 2023-01-16T10:04:06Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2023-08-01T12:47:32Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-022-00431-7
ec_funded: 1
external_id:
isi:
- '000862193600001'
file:
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checksum: 46352e0ee71e460848f88685ca852681
content_type: application/pdf
creator: dernst
date_created: 2023-02-02T11:01:10Z
date_updated: 2023-02-02T11:01:10Z
file_id: '12488'
file_name: 2023_DiscreteCompGeometry_Boissonnat.pdf
file_size: 582850
relation: main_file
success: 1
file_date_updated: 2023-02-02T11:01:10Z
has_accepted_license: '1'
intvolume: ' 69'
isi: 1
keyword:
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Theoretical Computer Science
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 156-191
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local criteria for triangulating general manifolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 69
year: '2023'
...
---
_id: '10623'
abstract:
- lang: eng
text: We investigate the BCS critical temperature Tc in the high-density limit and
derive an asymptotic formula, which strongly depends on the behavior of the interaction
potential V on the Fermi-surface. Our results include a rigorous confirmation
for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev
Lett 122:157001, 2019) and identify precise conditions under which superconducting
domes arise in BCS theory.
acknowledgement: I am very grateful to Robert Seiringer for his guidance during this
project and for many valuable comments on an earlier version of the manuscript.
Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions
and comments, pointing out the reference [22] and for his involvement in a closely
related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable
comments on an earlier version of the manuscript and Andreas Deuchert for interesting
discussions.
article_number: '3'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
citation:
ama: Henheik SJ. The BCS critical temperature at high density. Mathematical Physics,
Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0
apa: Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical
Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0
chicago: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical
Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0.
ieee: S. J. Henheik, “The BCS critical temperature at high density,” Mathematical
Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022.
ista: Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical
Physics, Analysis and Geometry. 25(1), 3.
mla: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical
Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022,
doi:10.1007/s11040-021-09415-0.
short: S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).
date_created: 2022-01-13T15:40:53Z
date_published: 2022-01-11T00:00:00Z
date_updated: 2023-08-02T13:51:52Z
day: '11'
ddc:
- '514'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11040-021-09415-0
ec_funded: 1
external_id:
arxiv:
- '2106.02015'
isi:
- '000741387600001'
file:
- access_level: open_access
checksum: d44f8123a52592a75b2c3b8ee2cd2435
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-14T07:27:45Z
date_updated: 2022-01-14T07:27:45Z
file_id: '10624'
file_name: 2022_MathPhyAnalGeo_Henheik.pdf
file_size: 505804
relation: main_file
success: 1
file_date_updated: 2022-01-14T07:27:45Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
issue: '1'
keyword:
- geometry and topology
- mathematical physics
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
eissn:
- 1572-9656
issn:
- 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The BCS critical temperature at high density
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: 25
year: '2022'
...
---
_id: '10643'
abstract:
- lang: eng
text: "We prove a generalised super-adiabatic theorem for extended fermionic systems
assuming a spectral gap only in the bulk. More precisely, we assume that the infinite
system has a unique ground state and that the corresponding Gelfand–Naimark–Segal
Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that
a similar adiabatic theorem also holds in the bulk of finite systems up to errors
that vanish faster than any inverse power of the system size, although the corresponding
finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"
acknowledgement: J.H. acknowledges partial financial support by the ERC Advanced Grant
‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft
and the Open Access Publishing Fund of the University of Tübingen is gratefully
acknowledged.
article_number: e4
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Stefan
full_name: Teufel, Stefan
last_name: Teufel
citation:
ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems
with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80'
apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic
limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2021.80'
chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2021.80.'
ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10.
Cambridge University Press, 2022.'
ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.'
mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol.
10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.'
short: S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).
date_created: 2022-01-18T16:18:51Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2023-08-02T13:53:11Z
day: '18'
ddc:
- '510'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1017/fms.2021.80
ec_funded: 1
external_id:
arxiv:
- '2012.15239'
isi:
- '000743615000001'
file:
- access_level: open_access
checksum: 87592a755adcef22ea590a99dc728dd3
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-19T09:27:43Z
date_updated: 2022-01-19T09:27:43Z
file_id: '10646'
file_name: 2022_ForumMathSigma_Henheik.pdf
file_size: 705323
relation: main_file
success: 1
file_date_updated: 2022-01-19T09:27:43Z
has_accepted_license: '1'
intvolume: ' 10'
isi: 1
keyword:
- computational mathematics
- discrete mathematics and combinatorics
- geometry and topology
- mathematical physics
- statistics and probability
- algebra and number theory
- theoretical computer science
- analysis
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk'
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: 10
year: '2022'
...
---
_id: '12129'
abstract:
- lang: eng
text: 'Given a finite point set P in general position in the plane, a full triangulation
of P is a maximal straight-line embedded plane graph on P. A partial triangulation
of P is a full triangulation of some subset P′ of P containing all extreme points
in P. A bistellar flip on a partial triangulation either flips an edge (called
edge flip), removes a non-extreme point of degree 3, or adds a point in P∖P′ as
vertex of degree 3. The bistellar flip graph has all partial triangulations as
vertices, and a pair of partial triangulations is adjacent if they can be obtained
from one another by a bistellar flip. The edge flip graph is defined with full
triangulations as vertices, and edge flips determining the adjacencies. Lawson
showed in the early seventies that these graphs are connected. The goal of this
paper is to investigate the structure of these graphs, with emphasis on their
vertex connectivity. For sets P of n points in the plane in general position,
we show that the edge flip graph is ⌈n/2−2⌉-vertex connected, and the bistellar
flip graph is (n−3)-vertex connected; both results are tight. The latter bound
matches the situation for the subfamily of regular triangulations (i.e., partial
triangulations obtained by lifting the points to 3-space and projecting back the
lower convex hull), where (n−3)-vertex connectivity has been known since the late
eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky
and Balinski’s Theorem. For the edge flip-graph, we additionally show that the
vertex connectivity is at least as large as (and hence equal to) the minimum degree
(i.e., the minimum number of flippable edges in any full triangulation), provided
that n is large enough. Our methods also yield several other results: (i) The
edge flip graph can be covered by graphs of polytopes of dimension ⌈n/2−2⌉ (products
of associahedra) and the bistellar flip graph can be covered by graphs of polytopes
of dimension n−3 (products of secondary polytopes). (ii) A partial triangulation
is regular, if it has distance n−3 in the Hasse diagram of the partial order of
partial subdivisions from the trivial subdivision. (iii) All partial triangulations
of a point set are regular iff the partial order of partial subdivisions has height
n−3. (iv) There are arbitrarily large sets P with non-regular partial triangulations
and such that every proper subset has only regular triangulations, i.e., there
are no small certificates for the existence of non-regular triangulations.'
acknowledgement: "This is a full and revised version of [38] (on partial triangulations)
in Proceedings of the 36th Annual International Symposium on Computational Geometry
(SoCG‘20) and of some of the results in [37] (on full triangulations) in Proceedings
of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA‘20).\r\nThis
research started at the 11th Gremo’s Workshop on Open Problems (GWOP), Alp Sellamatt,
Switzerland, June 24–28, 2013, motivated by a question posed by Filip Mori´c on
full triangulations. Research was supported by the Swiss National Science Foundation
within the collaborative DACH project Arrangements and Drawings as SNSF Project
200021E-171681, and by IST Austria and Berlin Free University during a sabbatical
stay of the second author. We thank Michael Joswig, Jesús De Loera, and Francisco
Santos for helpful discussions on the topics of this paper, and Daniel Bertschinger
and Valentin Stoppiello for carefully reading earlier versions and for many helpful
comments.\r\nOpen access funding provided by the Swiss Federal Institute of Technology
Zürich"
article_processing_charge: No
article_type: original
author:
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
- first_name: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane.
Discrete & Computational Geometry. 2022;68(4):1227-1284. doi:10.1007/s00454-022-00436-2
apa: Wagner, U., & Welzl, E. (2022). Connectivity of triangulation flip graphs
in the plane. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00436-2
chicago: Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs
in the Plane.” Discrete & Computational Geometry. Springer Nature,
2022. https://doi.org/10.1007/s00454-022-00436-2.
ieee: U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the
plane,” Discrete & Computational Geometry, vol. 68, no. 4. Springer
Nature, pp. 1227–1284, 2022.
ista: Wagner U, Welzl E. 2022. Connectivity of triangulation flip graphs in the
plane. Discrete & Computational Geometry. 68(4), 1227–1284.
mla: Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the
Plane.” Discrete & Computational Geometry, vol. 68, no. 4, Springer
Nature, 2022, pp. 1227–84, doi:10.1007/s00454-022-00436-2.
short: U. Wagner, E. Welzl, Discrete & Computational Geometry 68 (2022) 1227–1284.
date_created: 2023-01-12T12:02:28Z
date_published: 2022-11-14T00:00:00Z
date_updated: 2023-08-04T08:51:08Z
day: '14'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s00454-022-00436-2
external_id:
isi:
- '000883222200003'
file:
- access_level: open_access
checksum: 307e879d09e52eddf5b225d0aaa9213a
content_type: application/pdf
creator: dernst
date_created: 2023-01-23T11:10:03Z
date_updated: 2023-01-23T11:10:03Z
file_id: '12345'
file_name: 2022_DiscreteCompGeometry_Wagner.pdf
file_size: 1747581
relation: main_file
success: 1
file_date_updated: 2023-01-23T11:10:03Z
has_accepted_license: '1'
intvolume: ' 68'
isi: 1
issue: '4'
keyword:
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Theoretical Computer Science
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 1227-1284
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '7807'
relation: earlier_version
status: public
- id: '7990'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Connectivity of triangulation flip graphs in the plane
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: 68
year: '2022'
...
---
_id: '12148'
abstract:
- lang: eng
text: 'We prove a general local law for Wigner matrices that optimally handles observables
of arbitrary rank and thus unifies the well-known averaged and isotropic local
laws. As an application, we prove a central limit theorem in quantum unique ergodicity
(QUE): that is, we show that the quadratic forms of a general deterministic matrix
A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation.
For the bulk spectrum, we thus generalise our previous result [17] as valid for
test matrices A of large rank as well as the result of Benigni and Lopatto [7]
as valid for specific small-rank observables.'
acknowledgement: L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.
D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation
and the ETH Zürich Foundation.
article_number: e96
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices.
Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local
law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University
Press. https://doi.org/10.1017/fms.2022.86
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform
Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2022.86.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner
matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press,
2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner
matrices. Forum of Mathematics, Sigma. 10, e96.
mla: Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum
of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).
date_created: 2023-01-12T12:07:30Z
date_published: 2022-10-27T00:00:00Z
date_updated: 2023-08-04T09:00:35Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2022.86
ec_funded: 1
external_id:
isi:
- '000873719200001'
file:
- access_level: open_access
checksum: 94a049aeb1eea5497aa097712a73c400
content_type: application/pdf
creator: dernst
date_created: 2023-01-24T10:02:40Z
date_updated: 2023-01-24T10:02:40Z
file_id: '12356'
file_name: 2022_ForumMath_Cipolloni.pdf
file_size: 817089
relation: main_file
success: 1
file_date_updated: 2023-01-24T10:02:40Z
has_accepted_license: '1'
intvolume: ' 10'
isi: 1
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Mathematical Physics
- Statistics and Probability
- Algebra and Number Theory
- Theoretical Computer Science
- Analysis
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
issn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rank-uniform local law for Wigner matrices
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: 10
year: '2022'
...
---
_id: '12216'
abstract:
- lang: eng
text: Many trace inequalities can be expressed either as concavity/convexity theorems
or as monotonicity theorems. A classic example is the joint convexity of the quantum
relative entropy which is equivalent to the Data Processing Inequality. The latter
says that quantum operations can never increase the relative entropy. The monotonicity
versions often have many advantages, and often have direct physical application,
as in the example just mentioned. Moreover, the monotonicity results are often
valid for a larger class of maps than, say, quantum operations (which are completely
positive). In this paper we prove several new monotonicity results, the first
of which is a monotonicity theorem that has as a simple corollary a celebrated
concavity theorem of Epstein. Our starting points are the monotonicity versions
of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs
of these in their general forms using interpolation. We then prove our new monotonicity
theorems by several duality arguments.
acknowledgement: Work partially supported by the Lise Meitner fellowship, Austrian
Science Fund (FWF) M3337.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Eric A.
full_name: Carlen, Eric A.
last_name: Carlen
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and
related inequalities. Linear Algebra and its Applications. 2022;654:289-310.
doi:10.1016/j.laa.2022.09.001
apa: Carlen, E. A., & Zhang, H. (2022). Monotonicity versions of Epstein’s concavity
theorem and related inequalities. Linear Algebra and Its Applications.
Elsevier. https://doi.org/10.1016/j.laa.2022.09.001
chicago: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s
Concavity Theorem and Related Inequalities.” Linear Algebra and Its Applications.
Elsevier, 2022. https://doi.org/10.1016/j.laa.2022.09.001.
ieee: E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem
and related inequalities,” Linear Algebra and its Applications, vol. 654.
Elsevier, pp. 289–310, 2022.
ista: Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem
and related inequalities. Linear Algebra and its Applications. 654, 289–310.
mla: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity
Theorem and Related Inequalities.” Linear Algebra and Its Applications,
vol. 654, Elsevier, 2022, pp. 289–310, doi:10.1016/j.laa.2022.09.001.
short: E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.
date_created: 2023-01-16T09:46:38Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-04T09:24:51Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1016/j.laa.2022.09.001
external_id:
isi:
- '000860689600014'
file:
- access_level: open_access
checksum: cf3cb7e7e34baa967849f01d8f0c1ae4
content_type: application/pdf
creator: dernst
date_created: 2023-01-27T08:08:39Z
date_updated: 2023-01-27T08:08:39Z
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file_name: 2022_LinearAlgebra_Carlen.pdf
file_size: 441184
relation: main_file
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file_date_updated: 2023-01-27T08:08:39Z
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intvolume: ' 654'
isi: 1
keyword:
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Numerical Analysis
- Algebra and Number Theory
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 289-310
project:
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
publication: Linear Algebra and its Applications
publication_identifier:
issn:
- 0024-3795
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Monotonicity versions of Epstein's concavity theorem and related inequalities
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: 654
year: '2022'
...
---
_id: '12286'
abstract:
- lang: eng
text: "Inspired by the study of loose cycles in hypergraphs, we define the loose
core in hypergraphs as a structurewhich mirrors the close relationship between
cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random
hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition
at a certain critical threshold and determine this order, as well as the number
of edges, asymptotically in the subcritical and supercritical regimes.
\r\nOur
main tool is an algorithm called CoreConstruct, which enables us to analyse a
peeling process for the loose core. By analysing this algorithm we determine the
asymptotic degree distribution of vertices in the loose core and in particular
how many vertices and edges the loose core contains. As a corollary we obtain
an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$."
acknowledgement: 'Supported by Austrian Science Fund (FWF): I3747, W1230.'
article_number: P4.13
article_processing_charge: No
article_type: original
author:
- first_name: Oliver
full_name: Cooley, Oliver
id: 43f4ddd0-a46b-11ec-8df6-ef3703bd721d
last_name: Cooley
- first_name: Mihyun
full_name: Kang, Mihyun
last_name: Kang
- first_name: Julian
full_name: Zalla, Julian
last_name: Zalla
citation:
ama: Cooley O, Kang M, Zalla J. Loose cores and cycles in random hypergraphs. The
Electronic Journal of Combinatorics. 2022;29(4). doi:10.37236/10794
apa: Cooley, O., Kang, M., & Zalla, J. (2022). Loose cores and cycles in random
hypergraphs. The Electronic Journal of Combinatorics. The Electronic Journal
of Combinatorics. https://doi.org/10.37236/10794
chicago: Cooley, Oliver, Mihyun Kang, and Julian Zalla. “Loose Cores and Cycles
in Random Hypergraphs.” The Electronic Journal of Combinatorics. The Electronic
Journal of Combinatorics, 2022. https://doi.org/10.37236/10794.
ieee: O. Cooley, M. Kang, and J. Zalla, “Loose cores and cycles in random hypergraphs,”
The Electronic Journal of Combinatorics, vol. 29, no. 4. The Electronic
Journal of Combinatorics, 2022.
ista: Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs.
The Electronic Journal of Combinatorics. 29(4), P4.13.
mla: Cooley, Oliver, et al. “Loose Cores and Cycles in Random Hypergraphs.” The
Electronic Journal of Combinatorics, vol. 29, no. 4, P4.13, The Electronic
Journal of Combinatorics, 2022, doi:10.37236/10794.
short: O. Cooley, M. Kang, J. Zalla, The Electronic Journal of Combinatorics 29
(2022).
date_created: 2023-01-16T10:03:57Z
date_published: 2022-10-21T00:00:00Z
date_updated: 2023-08-04T10:29:18Z
day: '21'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.37236/10794
external_id:
isi:
- '000876763300001'
file:
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checksum: 00122b2459f09b5ae43073bfba565e94
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T11:45:13Z
date_updated: 2023-01-30T11:45:13Z
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file_name: 2022_ElecJournCombinatorics_Cooley_Kang_Zalla.pdf
file_size: 626953
relation: main_file
success: 1
file_date_updated: 2023-01-30T11:45:13Z
has_accepted_license: '1'
intvolume: ' 29'
isi: 1
issue: '4'
keyword:
- Computational Theory and Mathematics
- Geometry and Topology
- Theoretical Computer Science
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
publication: The Electronic Journal of Combinatorics
publication_identifier:
eissn:
- 1077-8926
publication_status: published
publisher: The Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Loose cores and cycles in random hypergraphs
tmp:
image: /image/cc_by_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
short: CC BY-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 29
year: '2022'
...
---
_id: '10856'
abstract:
- lang: eng
text: "We study the properties of the maximal volume k-dimensional sections of the
n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a
k-dimensional subspace to be a local maximizer of the volume of such sections,
which we formulate in a geometric way. We estimate the length of the projection
of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes
the volume of the intersection. We \x1Cnd the optimal upper bound on the volume
of a planar section of the cube [−1, 1]n , n ≥ 2."
acknowledgement: "The authors acknowledge the support of the grant of the Russian
Government N 075-15-\r\n2019-1926. G.I.was supported also by the SwissNational Science
Foundation grant 200021-179133. The authors are very grateful to the anonymous reviewer
for valuable remarks."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
- first_name: Igor
full_name: Tsiutsiurupa, Igor
last_name: Tsiutsiurupa
citation:
ama: Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. Analysis
and Geometry in Metric Spaces. 2021;9(1):1-18. doi:10.1515/agms-2020-0103
apa: Ivanov, G., & Tsiutsiurupa, I. (2021). On the volume of sections of the
cube. Analysis and Geometry in Metric Spaces. De Gruyter. https://doi.org/10.1515/agms-2020-0103
chicago: Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the
Cube.” Analysis and Geometry in Metric Spaces. De Gruyter, 2021. https://doi.org/10.1515/agms-2020-0103.
ieee: G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” Analysis
and Geometry in Metric Spaces, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021.
ista: Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis
and Geometry in Metric Spaces. 9(1), 1–18.
mla: Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.”
Analysis and Geometry in Metric Spaces, vol. 9, no. 1, De Gruyter, 2021,
pp. 1–18, doi:10.1515/agms-2020-0103.
short: G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021)
1–18.
date_created: 2022-03-18T09:25:14Z
date_published: 2021-01-29T00:00:00Z
date_updated: 2023-08-17T07:07:58Z
day: '29'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1515/agms-2020-0103
external_id:
arxiv:
- '2004.02674'
isi:
- '000734286800001'
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- access_level: open_access
checksum: 7e615ac8489f5eae580b6517debfdc53
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creator: dernst
date_created: 2022-03-18T09:31:59Z
date_updated: 2022-03-18T09:31:59Z
file_id: '10857'
file_name: 2021_AnalysisMetricSpaces_Ivanov.pdf
file_size: 789801
relation: main_file
success: 1
file_date_updated: 2022-03-18T09:31:59Z
has_accepted_license: '1'
intvolume: ' 9'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Geometry and Topology
- Analysis
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 1-18
publication: Analysis and Geometry in Metric Spaces
publication_identifier:
issn:
- 2299-3274
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the volume of sections of the cube
tmp:
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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: 9
year: '2021'
...
---
_id: '11446'
abstract:
- lang: eng
text: Suppose that n is not a prime power and not twice a prime power. We prove
that for any Hausdorff compactum X with a free action of the symmetric group Sn,
there exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}.
Previously, the special cases of this statement for certain X were usually proved
using the equivartiant obstruction theory. Such calculations are difficult and
may become infeasible past the first (primary) obstruction. We take a different
approach which allows us to prove the vanishing of all obstructions simultaneously.
The essential step in the proof is classifying the possible degrees of Sn-equivariant
maps from the boundary ∂Δn−1 of (n−1)-simplex to itself. Existence of equivariant
maps between spaces is important for many questions arising from discrete mathematics
and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting
Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate
the utility of our result applying it to one such question, a specific instance
of envy-free division problem.
acknowledgement: S. Avvakumov has received funding from the European Research Council
under the European Union’s Seventh Framework Programme ERC Grant agreement ERC StG
716424–CASe. S. Kudrya was supported by the Austrian Academic Exchange Service (OeAD),
ICM-2019-13577.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
- first_name: Sergey
full_name: Kudrya, Sergey
id: ecf01965-d252-11ea-95a5-8ada5f6c6a67
last_name: Kudrya
citation:
ama: Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping
degree. Discrete & Computational Geometry. 2021;66(3):1202-1216. doi:10.1007/s00454-021-00299-z
apa: Avvakumov, S., & Kudrya, S. (2021). Vanishing of all equivariant obstructions
and the mapping degree. Discrete & Computational Geometry. Springer
Nature. https://doi.org/10.1007/s00454-021-00299-z
chicago: Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions
and the Mapping Degree.” Discrete & Computational Geometry. Springer
Nature, 2021. https://doi.org/10.1007/s00454-021-00299-z.
ieee: S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and
the mapping degree,” Discrete & Computational Geometry, vol. 66, no.
3. Springer Nature, pp. 1202–1216, 2021.
ista: Avvakumov S, Kudrya S. 2021. Vanishing of all equivariant obstructions and
the mapping degree. Discrete & Computational Geometry. 66(3), 1202–1216.
mla: Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions
and the Mapping Degree.” Discrete & Computational Geometry, vol. 66,
no. 3, Springer Nature, 2021, pp. 1202–16, doi:10.1007/s00454-021-00299-z.
short: S. Avvakumov, S. Kudrya, Discrete & Computational Geometry 66 (2021)
1202–1216.
date_created: 2022-06-17T08:45:15Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2023-02-23T13:26:41Z
day: '01'
doi: 10.1007/s00454-021-00299-z
extern: '1'
external_id:
arxiv:
- '1910.12628'
intvolume: ' 66'
issue: '3'
keyword:
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Theoretical Computer Science
language:
- iso: eng
month: '10'
oa_version: Preprint
page: 1202-1216
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '8182'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Vanishing of all equivariant obstructions and the mapping degree
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 66
year: '2021'
...
---
_id: '8940'
abstract:
- lang: eng
text: We quantise Whitney’s construction to prove the existence of a triangulation
for any C^2 manifold, so that we get an algorithm with explicit bounds. We also
give a new elementary proof, which is completely geometric.
acknowledgement: This work has been funded by the European Research Council under
the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations
of Geometric Understanding in Higher Dimensions). The third author also received
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding
provided by the Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Jean-Daniel
full_name: Boissonnat, Jean-Daniel
last_name: Boissonnat
- first_name: Siargey
full_name: Kachanovich, Siargey
last_name: Kachanovich
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds:
An elementary and quantified version of Whitney’s method. Discrete & Computational
Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8'
apa: 'Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating
submanifolds: An elementary and quantified version of Whitney’s method. Discrete
& Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8'
chicago: 'Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken.
“Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s
Method.” Discrete & Computational Geometry. Springer Nature, 2021.
https://doi.org/10.1007/s00454-020-00250-8.'
ieee: 'J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds:
An elementary and quantified version of Whitney’s method,” Discrete & Computational
Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.'
ista: 'Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds:
An elementary and quantified version of Whitney’s method. Discrete & Computational
Geometry. 66(1), 386–434.'
mla: 'Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary
and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry,
vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.'
short: J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational
Geometry 66 (2021) 386–434.
date_created: 2020-12-12T11:07:02Z
date_published: 2021-07-01T00:00:00Z
date_updated: 2023-09-05T15:02:40Z
day: '01'
ddc:
- '516'
department:
- _id: HeEd
doi: 10.1007/s00454-020-00250-8
ec_funded: 1
external_id:
isi:
- '000597770300001'
file:
- access_level: open_access
checksum: c848986091e56699dc12de85adb1e39c
content_type: application/pdf
creator: kschuh
date_created: 2021-08-06T09:52:29Z
date_updated: 2021-08-06T09:52:29Z
file_id: '9795'
file_name: 2021_DescreteCompGeopmetry_Boissonnat.pdf
file_size: 983307
relation: main_file
success: 1
file_date_updated: 2021-08-06T09:52:29Z
has_accepted_license: '1'
intvolume: ' 66'
isi: 1
issue: '1'
keyword:
- Theoretical Computer Science
- Computational Theory and Mathematics
- Geometry and Topology
- Discrete Mathematics and Combinatorics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 386-434
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: 'Triangulating submanifolds: An elementary and quantified version of Whitney’s
method'
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: 66
year: '2021'
...
---
_id: '8422'
abstract:
- lang: eng
text: 'The Birkhoff conjecture says that the boundary of a strictly convex integrable
billiard table is necessarily an ellipse. In this article, we consider a stronger
notion of integrability, namely integrability close to the boundary, and prove
a local version of this conjecture: a small perturbation of an ellipse of small
eccentricity which preserves integrability near the boundary, is itself an ellipse.
This extends the result in Avila et al. (Ann Math 184:527–558, ADK16), where integrability
was assumed on a larger set. In particular, it shows that (local) integrability
near the boundary implies global integrability. One of the crucial ideas in the
proof consists in analyzing Taylor expansion of the corresponding action-angle
coordinates with respect to the eccentricity parameter, deriving and studying
higher order conditions for the preservation of integrable rational caustics.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guan
full_name: Huang, Guan
last_name: Huang
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Alfonso
full_name: Sorrentino, Alfonso
last_name: Sorrentino
citation:
ama: Huang G, Kaloshin V, Sorrentino A. Nearly circular domains which are integrable
close to the boundary are ellipses. Geometric and Functional Analysis.
2018;28(2):334-392. doi:10.1007/s00039-018-0440-4
apa: Huang, G., Kaloshin, V., & Sorrentino, A. (2018). Nearly circular domains
which are integrable close to the boundary are ellipses. Geometric and Functional
Analysis. Springer Nature. https://doi.org/10.1007/s00039-018-0440-4
chicago: Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “Nearly Circular Domains
Which Are Integrable Close to the Boundary Are Ellipses.” Geometric and Functional
Analysis. Springer Nature, 2018. https://doi.org/10.1007/s00039-018-0440-4.
ieee: G. Huang, V. Kaloshin, and A. Sorrentino, “Nearly circular domains which are
integrable close to the boundary are ellipses,” Geometric and Functional Analysis,
vol. 28, no. 2. Springer Nature, pp. 334–392, 2018.
ista: Huang G, Kaloshin V, Sorrentino A. 2018. Nearly circular domains which are
integrable close to the boundary are ellipses. Geometric and Functional Analysis.
28(2), 334–392.
mla: Huang, Guan, et al. “Nearly Circular Domains Which Are Integrable Close to
the Boundary Are Ellipses.” Geometric and Functional Analysis, vol. 28,
no. 2, Springer Nature, 2018, pp. 334–92, doi:10.1007/s00039-018-0440-4.
short: G. Huang, V. Kaloshin, A. Sorrentino, Geometric and Functional Analysis 28
(2018) 334–392.
date_created: 2020-09-17T10:42:30Z
date_published: 2018-03-18T00:00:00Z
date_updated: 2021-01-12T08:19:11Z
day: '18'
doi: 10.1007/s00039-018-0440-4
extern: '1'
external_id:
arxiv:
- '1705.10601'
intvolume: ' 28'
issue: '2'
keyword:
- Geometry and Topology
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.10601
month: '03'
oa: 1
oa_version: Preprint
page: 334-392
publication: Geometric and Functional Analysis
publication_identifier:
issn:
- 1016-443X
- 1420-8970
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Nearly circular domains which are integrable close to the boundary are ellipses
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2018'
...