---
OA_place: repository
OA_type: green
_id: '19425'
abstract:
- lang: eng
text: "We demonstrate that periodically driven quantum rotors provide a promising
and broadly applicable platform to implement multi-gap topological phases, where
groups of bands can acquire topological invariants due to non-Abelian braiding
of band degeneracies. By adiabatically varying the periodic kicks to the rotor
we find nodal-line braiding, which causes sign flips of topological charges of
band nodes and can prevent them from annihilating, indicated by non-zero values
of the %non-Abelian patch Euler class. In particular, we report\r\non the emergence
of an anomalous Dirac string phase arising in the strongly driven regime, a truly
out-of-equilibrium phase of the quantum rotor. This phase emanates from braiding
processes involving all (quasienergy) gaps and manifests itself with edge states
at zero angular momentum. Our results reveal direct applications in state-of-the-art
experiments of quantum rotors, such as linear molecules driven by periodic far-off-resonant
laser pulses or artificial\r\nquantum rotors in optical lattices, whose extensive
versatility offers precise modification and observation of novel non-Abelian topological
properties. "
acknowledgement: "We thank G. M. Koutentakis, S. Wimberger, J. G. E. Harris, T. Enss
and A. Ghazaryan for fruitful discussions. M.L. acknowledges support by the European
Research Council (ERC) Starting Grant No. 801770 (ANGULON). R.-J. S. acknowledges
funding from a EPSRC ERC underwrite grant EP/X025829/1, a EPSRC New Investigator
Award grant EP/W00187X/1, as well as Trinity College, Cambridge. F.N.U. acknowledges
support from the Marie ¨Sk lodowska-Curie programme of the European Commission [Grant
No. 893915], Simons Investigator Award\r\n[Grant No. 511029] and Trinity College
Cambridge."
article_number: '2408.16848'
article_processing_charge: No
arxiv: 1
author:
- first_name: Volker
full_name: Karle, Volker
id: D7C012AE-D7ED-11E9-95E8-1EC5E5697425
last_name: Karle
orcid: 0000-0002-6963-0129
- first_name: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: Adrien
full_name: Bouhon, Adrien
last_name: Bouhon
- first_name: Robert-Jan
full_name: Slager, Robert-Jan
last_name: Slager
- first_name: F. Nur
full_name: Ünal, F. Nur
last_name: Ünal
citation:
ama: Karle V, Lemeshko M, Bouhon A, Slager R-J, Ünal FN. Anomalous multi-gap topological
phases in periodically driven quantum rotors. arXiv. doi:10.48550/arXiv.2408.16848
apa: Karle, V., Lemeshko, M., Bouhon, A., Slager, R.-J., & Ünal, F. N. (n.d.).
Anomalous multi-gap topological phases in periodically driven quantum rotors.
arXiv. https://doi.org/10.48550/arXiv.2408.16848
chicago: Karle, Volker, Mikhail Lemeshko, Adrien Bouhon, Robert-Jan Slager, and
F. Nur Ünal. “Anomalous Multi-Gap Topological Phases in Periodically Driven Quantum
Rotors.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2408.16848.
ieee: V. Karle, M. Lemeshko, A. Bouhon, R.-J. Slager, and F. N. Ünal, “Anomalous
multi-gap topological phases in periodically driven quantum rotors,” arXiv.
.
ista: Karle V, Lemeshko M, Bouhon A, Slager R-J, Ünal FN. Anomalous multi-gap topological
phases in periodically driven quantum rotors. arXiv, 2408.16848.
mla: Karle, Volker, et al. “Anomalous Multi-Gap Topological Phases in Periodically
Driven Quantum Rotors.” ArXiv, 2408.16848, doi:10.48550/arXiv.2408.16848.
short: V. Karle, M. Lemeshko, A. Bouhon, R.-J. Slager, F.N. Ünal, ArXiv (n.d.).
date_created: 2025-03-20T07:48:23Z
date_published: 2024-08-29T00:00:00Z
date_updated: 2026-07-29T08:59:31Z
day: '29'
department:
- _id: MiLe
doi: 10.48550/arXiv.2408.16848
ec_funded: 1
external_id:
arxiv:
- '2408.16848'
fulldoi: https://doi.org/10.48550/arXiv.2408.16848
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.48550/arXiv.2408.16848
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '801770'
name: 'Angulon: physics and applications of a new quasiparticle'
publication: arXiv
publication_status: draft
related_material:
record:
- id: '19393'
relation: dissertation_contains
status: public
- id: '21009'
relation: later_version
status: public
status: public
title: Anomalous multi-gap topological phases in periodically driven quantum rotors
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '17127'
abstract:
- lang: eng
text: "Let P(x)∈Z[x] be a polynomial with at least two distinct complex roots.
We prove that the number of solutions (x1,…,xk,y1,…,yk)∈[N]2k to the equation\r\n∏1≤i≤kP(xi)=∏1≤j≤kP(yj)≠0\r\n(for
any k≥1 ) is asymptotically k!Nk as N→+∞. This solves a question first proposed
and studied by Najnudel. The result can also be interpreted as saying that all
even moments of random partial sums 1N√∑n≤Nf(P(n)) match standard complex Gaussian
moments as N→+∞\r\n , where f is the Steinhaus random multiplicative function."
acknowledgement: 'We thank Oleksiy Klurman, Ilya Shkredov, and Igor Shparlinski for
helpful comments on earlier versions of the paper, and thank Yotam Hendel for providing
a reference for Lemma 2.1. We also thank the anonymous referee for their generous
corrections and comments. The first author has received funding from the European
Union''s Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie
Grant Agreement Number: 101034413. The second author is partially supported by the
Cuthbert C. Hurd Graduate Fellowship in the Mathematical Sciences, Stanford.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Victor
full_name: Wang, Victor
id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
last_name: Wang
orcid: 0000-0002-0704-7026
- first_name: Max Wenqiang
full_name: Xu, Max Wenqiang
last_name: Xu
citation:
ama: Wang V, Xu MW. Paucity phenomena for polynomial products. Bulletin of the
London Mathematical Society. 2024;56(8):2718-2726. doi:10.1112/blms.13095
apa: Wang, V., & Xu, M. W. (2024). Paucity phenomena for polynomial products.
Bulletin of the London Mathematical Society. London Mathematical Society.
https://doi.org/10.1112/blms.13095
chicago: Wang, Victor, and Max Wenqiang Xu. “Paucity Phenomena for Polynomial Products.”
Bulletin of the London Mathematical Society. London Mathematical Society,
2024. https://doi.org/10.1112/blms.13095.
ieee: V. Wang and M. W. Xu, “Paucity phenomena for polynomial products,” Bulletin
of the London Mathematical Society, vol. 56, no. 8. London Mathematical Society,
pp. 2718–2726, 2024.
ista: Wang V, Xu MW. 2024. Paucity phenomena for polynomial products. Bulletin of
the London Mathematical Society. 56(8), 2718–2726.
mla: Wang, Victor, and Max Wenqiang Xu. “Paucity Phenomena for Polynomial Products.”
Bulletin of the London Mathematical Society, vol. 56, no. 8, London Mathematical
Society, 2024, pp. 2718–26, doi:10.1112/blms.13095.
short: V. Wang, M.W. Xu, Bulletin of the London Mathematical Society 56 (2024) 2718–2726.
das_tickbox: '0'
date_created: 2024-06-09T22:01:03Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2026-07-29T09:57:59Z
day: '01'
ddc:
- '512'
department:
- _id: TiBr
doi: 10.1112/blms.13095
ec_funded: 1
external_id:
arxiv:
- '2211.02908'
isi:
- '001235729900001'
file:
- access_level: open_access
checksum: ae386a4031856efac23c7cdcb53b559b
content_type: application/pdf
creator: vwang
date_created: 2024-08-20T08:36:32Z
date_updated: 2024-08-20T08:36:32Z
file_id: '17446'
file_name: Paucity_phenomena_for_polynomial_products__Wang_Xu_ (7).pdf
file_size: 331775
relation: main_file
success: 1
file_date_updated: 2024-08-20T08:36:32Z
fulldoi: https://doi.org/10.1112/blms.13095
has_accepted_license: '1'
intvolume: ' 56'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2211.02908
month: '08'
oa: 1
oa_version: Submitted Version
page: 2718-2726
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- 1469-2120
issn:
- 0024-6093
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Paucity phenomena for polynomial products
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 56
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15338'
abstract:
- lang: eng
text: We introduce a new class of generalised quadratic forms over totally real
number fields, which is rich enough to capture the arithmetic of arbitrary systems
of quadrics over the rational numbers. We explore this connection through a version
of the Hardy–Littlewood circle method over number fields.
acknowledgement: The authors are grateful to Jayce Getz for asking questions that
set this project in motion and to the anonymous referee for useful comments. T.B.
was supported by a FWF grant (DOI 10.55776/P32428) and by a grant from the Institute
for Advanced Study School of Mathematics. L.B.P. was partially supported by NSF
DMS-2200470 and DMS-1652173, and thanks the Hausdorff Centre for Mathematics for
hosting research visits.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Lillian B.
full_name: Pierce, Lillian B.
last_name: Pierce
- first_name: Damaris
full_name: Schindler, Damaris
last_name: Schindler
citation:
ama: Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally
real number fields. Journal of the Institute of Mathematics of Jussieu.
2024;23(6):2859-2912. doi:10.1017/S1474748024000161
apa: Browning, T. D., Pierce, L. B., & Schindler, D. (2024). Generalised quadratic
forms over totally real number fields. Journal of the Institute of Mathematics
of Jussieu. Cambridge University Press. https://doi.org/10.1017/S1474748024000161
chicago: Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised
Quadratic Forms over Totally Real Number Fields.” Journal of the Institute
of Mathematics of Jussieu. Cambridge University Press, 2024. https://doi.org/10.1017/S1474748024000161.
ieee: T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms
over totally real number fields,” Journal of the Institute of Mathematics of
Jussieu, vol. 23, no. 6. Cambridge University Press, pp. 2859–2912, 2024.
ista: Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over
totally real number fields. Journal of the Institute of Mathematics of Jussieu.
23(6), 2859–2912.
mla: Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real
Number Fields.” Journal of the Institute of Mathematics of Jussieu, vol.
23, no. 6, Cambridge University Press, 2024, pp. 2859–912, doi:10.1017/S1474748024000161.
short: T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics
of Jussieu 23 (2024) 2859–2912.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2026-07-29T09:57:08Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/S1474748024000161
external_id:
arxiv:
- '2212.11038'
isi:
- '001200337400001'
file:
- access_level: open_access
checksum: b300541d581a71d92314df5ae8c4cc09
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:56:33Z
date_updated: 2025-01-09T08:56:33Z
file_id: '18793'
file_name: 2024_JournInstMathJussieu_Browning.pdf
file_size: 690974
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:56:33Z
fulldoi: https://doi.org/10.1017/S1474748024000161
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '6'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 2859-2912
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
eissn:
- 1475-3030
issn:
- 1474-7480
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Generalised quadratic forms over totally real number fields
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 23
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15337'
abstract:
- lang: eng
text: We prove the Manin–Peyre conjecture for the number of rational points of bounded
height outside of a thin subset on a family of Fano threefolds of bidegree (1,
2).
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).The authors are grateful to Florian Wilsch for useful comments. While
working on this paper the authors were supported by FWF grant P 32428.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Dante
full_name: Bonolis, Dante
id: 6A459894-5FDD-11E9-AF35-BB24E6697425
last_name: Bonolis
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Zhizhong
full_name: Huang, Zhizhong
id: 21f1b52f-2fd1-11eb-a347-a4cdb9b18a51
last_name: Huang
citation:
ama: Bonolis D, Browning TD, Huang Z. Density of rational points on some quadric
bundle threefolds. Mathematische Annalen. 2024;390:4123-4207. doi:10.1007/s00208-024-02854-4
apa: Bonolis, D., Browning, T. D., & Huang, Z. (2024). Density of rational points
on some quadric bundle threefolds. Mathematische Annalen. Springer Nature.
https://doi.org/10.1007/s00208-024-02854-4
chicago: Bonolis, Dante, Timothy D Browning, and Zhizhong Huang. “Density of Rational
Points on Some Quadric Bundle Threefolds.” Mathematische Annalen. Springer
Nature, 2024. https://doi.org/10.1007/s00208-024-02854-4.
ieee: D. Bonolis, T. D. Browning, and Z. Huang, “Density of rational points on some
quadric bundle threefolds,” Mathematische Annalen, vol. 390. Springer Nature,
pp. 4123–4207, 2024.
ista: Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some
quadric bundle threefolds. Mathematische Annalen. 390, 4123–4207.
mla: Bonolis, Dante, et al. “Density of Rational Points on Some Quadric Bundle Threefolds.”
Mathematische Annalen, vol. 390, Springer Nature, 2024, pp. 4123–207, doi:10.1007/s00208-024-02854-4.
short: D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2026-07-29T09:56:42Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00208-024-02854-4
external_id:
arxiv:
- '2204.09322'
isi:
- '001204670500001'
file:
- access_level: open_access
checksum: 5dd51531deb1e4760c38c3c0c7d5aedc
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T09:08:14Z
date_updated: 2025-01-09T09:08:14Z
file_id: '18796'
file_name: 2024_MathAnnalen_Bonolis.pdf
file_size: 1019116
relation: main_file
success: 1
file_date_updated: 2025-01-09T09:08:14Z
fulldoi: https://doi.org/10.1007/s00208-024-02854-4
has_accepted_license: '1'
intvolume: ' 390'
isi: 1
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 4123-4207
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
status: public
supplementarymaterial: no
title: Density of rational points on some quadric bundle threefolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 390
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '18930'
abstract:
- lang: eng
text: "We study sumsets \U0001D49C + ℬ in the set of squares \U0001D4AE (and, more
generally, in the set of kth powers \U0001D4AEk, where k ≥2 is an integer). It
is known by a result of Gyarmati that \U0001D49C + ℬ ⊂ \U0001D4AEk ∩[1,N] implies
that min(|\U0001D49C|,|ℬ|) =Ok(logN). Here, we study how the upper bound on |ℬ|
decreases, when the size of |\U0001D49C| increases (or vice versa). In particular,
if |\U0001D49C| ≥ Ck1m m(logN)1m , then |ℬ| = Ok(m2logN), for sufficiently large
N, a positive integer m and an explicit constant C > 0. For example, with m ∼
loglogN this gives: If |\U0001D49C| ≥ CkloglogN,then |ℬ| = Ok(logN(loglogN)2)."
acknowledgement: This manuscript grew out of the second author’s MSc Thesis at Graz
University of Technology [34]. C. Elsholtz is supported by a joint FWF-ANR project
ArithRand, grant numbers FWF I 4945-N and ANR-20-CE91-0006. Both authors would like
to thank Igor Shparlinski for drawing our attention to related character sum estimates.
Furthermore, we would like to thank the referee for a careful reading of the paper.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Christian
full_name: Elsholtz, Christian
last_name: Elsholtz
- first_name: Lena
full_name: Wurzinger, Lena
id: 50c57d72-32a8-11ee-aeea-d652094d2ccd
last_name: Wurzinger
orcid: 0009-0004-5360-0074
citation:
ama: Elsholtz C, Wurzinger L. Sumsets in the set of squares. The Quarterly Journal
of Mathematics. 2024;75(4):1243-1254. doi:10.1093/qmath/haae044
apa: Elsholtz, C., & Wurzinger, L. (2024). Sumsets in the set of squares. The
Quarterly Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qmath/haae044
chicago: Elsholtz, Christian, and Lena Wurzinger. “Sumsets in the Set of Squares.”
The Quarterly Journal of Mathematics. Oxford University Press, 2024. https://doi.org/10.1093/qmath/haae044.
ieee: C. Elsholtz and L. Wurzinger, “Sumsets in the set of squares,” The Quarterly
Journal of Mathematics, vol. 75, no. 4. Oxford University Press, pp. 1243–1254,
2024.
ista: Elsholtz C, Wurzinger L. 2024. Sumsets in the set of squares. The Quarterly
Journal of Mathematics. 75(4), 1243–1254.
mla: Elsholtz, Christian, and Lena Wurzinger. “Sumsets in the Set of Squares.” The
Quarterly Journal of Mathematics, vol. 75, no. 4, Oxford University Press,
2024, pp. 1243–54, doi:10.1093/qmath/haae044.
short: C. Elsholtz, L. Wurzinger, The Quarterly Journal of Mathematics 75 (2024)
1243–1254.
corr_author: '1'
das_tickbox: '0'
date_created: 2025-01-28T06:55:31Z
date_published: 2024-12-01T00:00:00Z
date_updated: 2026-07-29T09:58:28Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1093/qmath/haae044
external_id:
isi:
- '001304396600001'
file:
- access_level: open_access
checksum: 1a06e052761d3f1e873463d6f529dd82
content_type: application/pdf
creator: dernst
date_created: 2025-01-28T07:03:51Z
date_updated: 2025-01-28T07:03:51Z
file_id: '18931'
file_name: 2024_QuarterlyJourMath_Elsholtz.pdf
file_size: 424645
relation: main_file
success: 1
file_date_updated: 2025-01-28T07:03:51Z
fulldoi: https://doi.org/10.1093/qmath/haae044
has_accepted_license: '1'
intvolume: ' 75'
isi: 1
issue: '4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1243-1254
publication: The Quarterly Journal of Mathematics
publication_identifier:
eissn:
- 1464-3847
issn:
- 0033-5606
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Sumsets in the set of squares
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 75
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15312'
abstract:
- lang: eng
text: The question of whether or not a given integral polynomial takes infinitely
many square-free values has only been addressed unconditionally for polynomials
of degree at most 3. We address this question, on average, for polynomials of
arbitrary degree.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Igor E.
full_name: Shparlinski, Igor E.
last_name: Shparlinski
citation:
ama: Browning TD, Shparlinski IE. Square-free values of random polynomials. Journal
of Number Theory. 2024;261:220-240. doi:10.1016/j.jnt.2024.02.013
apa: Browning, T. D., & Shparlinski, I. E. (2024). Square-free values of random
polynomials. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2024.02.013
chicago: Browning, Timothy D, and Igor E. Shparlinski. “Square-Free Values of Random
Polynomials.” Journal of Number Theory. Elsevier, 2024. https://doi.org/10.1016/j.jnt.2024.02.013.
ieee: T. D. Browning and I. E. Shparlinski, “Square-free values of random polynomials,”
Journal of Number Theory, vol. 261. Elsevier, pp. 220–240, 2024.
ista: Browning TD, Shparlinski IE. 2024. Square-free values of random polynomials.
Journal of Number Theory. 261, 220–240.
mla: Browning, Timothy D., and Igor E. Shparlinski. “Square-Free Values of Random
Polynomials.” Journal of Number Theory, vol. 261, Elsevier, 2024, pp. 220–40,
doi:10.1016/j.jnt.2024.02.013.
short: T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240.
corr_author: '1'
das_tickbox: '0'
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- '510'
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doi: 10.1016/j.jnt.2024.02.013
external_id:
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- '001220725000001'
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title: Square-free values of random polynomials
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...
---
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_id: '19051'
abstract:
- lang: eng
text: This paper corrects an error in an earlier work of the author.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: Browning TD. The polynomial sieve and equal sums of like polynomials. International
Mathematics Research Notices. 2024;2024(13):10165-10168. doi:10.1093/imrn/rnae066
apa: Browning, T. D. (2024). The polynomial sieve and equal sums of like polynomials.
International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae066
chicago: Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.”
International Mathematics Research Notices. Oxford University Press, 2024.
https://doi.org/10.1093/imrn/rnae066.
ieee: T. D. Browning, “The polynomial sieve and equal sums of like polynomials,”
International Mathematics Research Notices, vol. 2024, no. 13. Oxford University
Press, pp. 10165–10168, 2024.
ista: Browning TD. 2024. The polynomial sieve and equal sums of like polynomials.
International Mathematics Research Notices. 2024(13), 10165–10168.
mla: Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.”
International Mathematics Research Notices, vol. 2024, no. 13, Oxford University
Press, 2024, pp. 10165–68, doi:10.1093/imrn/rnae066.
short: T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168.
corr_author: '1'
das_tickbox: '0'
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- iso: eng
month: '07'
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publisher: Oxford University Press
quality_controlled: '1'
related_material:
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title: The polynomial sieve and equal sums of like polynomials
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year: '2024'
...
---
_id: '10018'
abstract:
- lang: eng
text: In order to study integral points of bounded log-anticanonical height on weak
del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example,
we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove
an analogue of Manin's conjecture for integral points with respect to its singularities
and its lines.
acknowledgement: The first author was partly supported by grant DE 1646/4-2 of the
Deutsche Forschungsgemeinschaft. The second author was partly supported by FWF grant
P 32428-N35 and conducted part of this work as a guest at the Institut de Mathématiques
de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Ulrich
full_name: Derenthal, Ulrich
last_name: Derenthal
- first_name: Florian Alexander
full_name: Wilsch, Florian Alexander
id: 560601DA-8D36-11E9-A136-7AC1E5697425
last_name: Wilsch
orcid: 0000-0001-7302-8256
citation:
ama: Derenthal U, Wilsch FA. Integral points on singular del Pezzo surfaces. Journal
of the Institute of Mathematics of Jussieu. 2024;23(3):1259-1294. doi:10.1017/S1474748022000482
apa: Derenthal, U., & Wilsch, F. A. (2024). Integral points on singular del
Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu. Cambridge
University Press. https://doi.org/10.1017/S1474748022000482
chicago: Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular
Del Pezzo Surfaces.” Journal of the Institute of Mathematics of Jussieu.
Cambridge University Press, 2024. https://doi.org/10.1017/S1474748022000482.
ieee: U. Derenthal and F. A. Wilsch, “Integral points on singular del Pezzo surfaces,”
Journal of the Institute of Mathematics of Jussieu, vol. 23, no. 3. Cambridge
University Press, pp. 1259–1294, 2024.
ista: Derenthal U, Wilsch FA. 2024. Integral points on singular del Pezzo surfaces.
Journal of the Institute of Mathematics of Jussieu. 23(3), 1259–1294.
mla: Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular
Del Pezzo Surfaces.” Journal of the Institute of Mathematics of Jussieu,
vol. 23, no. 3, Cambridge University Press, 2024, pp. 1259–94, doi:10.1017/S1474748022000482.
short: U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu
23 (2024) 1259–1294.
corr_author: '1'
das_tickbox: '0'
date_created: 2021-09-15T10:06:48Z
date_published: 2024-05-10T00:00:00Z
date_updated: 2026-07-29T10:00:51Z
day: '10'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/S1474748022000482
external_id:
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- '2109.06778'
isi:
- '000881319200001'
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intvolume: ' 23'
isi: 1
issue: '3'
keyword:
- Integral points
- del Pezzo surface
- universal torsor
- Manin’s conjecture
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1259-1294
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
eissn:
- '1475-3030 '
issn:
- 1474-7480
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
researchdata_availability: no
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status: public
supplementarymaterial: no
title: Integral points on singular del Pezzo surfaces
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type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 23
year: '2024'
...
---
_id: '17447'
abstract:
- lang: eng
text: Let F be a diagonal cubic form over Z in six variables. From the dual variety
in the delta method of Duke–Friedlander–Iwaniec and Heath‐Brown, we unconditionally
extract a weighted count of certain special integral zeros of F in regions of
diameter X - 8 . Heath‐Brown did the same in four variables, but our analysis
differs and captures some novel features. We also put forth an axiomatic framework
for more general F.
acknowledgement: This paper is an important component of the thesis work described
in [25]; many of my acknowledgements there apply here as well. I also thank my advisor,
Peter Sarnak, for many helpful suggestions and questions on the exposition, references,
assumptions, and scope of (various drafts of) the present work. I am also grateful
to Trevor Wooley for providing some helpful general comments on special subvarieties
and the reference [24]. I thank Tim Browning for inspiring part of the current title
of the paper. Finally, thanks are due to the referee for providing many helpful
suggestions. This work was partially supported by NSF grant DMS-1802211, and the
European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie
Grant AgreementNo. 101034413.
article_number: e12975
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Victor
full_name: Wang, Victor
id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
last_name: Wang
orcid: 0000-0002-0704-7026
citation:
ama: Wang V. Special cubic zeros and the dual variety. Journal of the London
Mathematical Society. 2024;110(3). doi:10.1112/jlms.12975
apa: Wang, V. (2024). Special cubic zeros and the dual variety. Journal of the
London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12975
chicago: Wang, Victor. “Special Cubic Zeros and the Dual Variety.” Journal of
the London Mathematical Society. Wiley, 2024. https://doi.org/10.1112/jlms.12975.
ieee: V. Wang, “Special cubic zeros and the dual variety,” Journal of the London
Mathematical Society, vol. 110, no. 3. Wiley, 2024.
ista: Wang V. 2024. Special cubic zeros and the dual variety. Journal of the London
Mathematical Society. 110(3), e12975.
mla: Wang, Victor. “Special Cubic Zeros and the Dual Variety.” Journal of the
London Mathematical Society, vol. 110, no. 3, e12975, Wiley, 2024, doi:10.1112/jlms.12975.
short: V. Wang, Journal of the London Mathematical Society 110 (2024).
corr_author: '1'
das_tickbox: '0'
date_created: 2024-08-20T08:41:40Z
date_published: 2024-08-14T00:00:00Z
date_updated: 2026-07-29T10:02:22Z
day: '14'
ddc:
- '512'
department:
- _id: TiBr
doi: 10.1112/jlms.12975
ec_funded: 1
external_id:
arxiv:
- '2108.03396'
isi:
- '001310529600001'
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relation: main_file
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fulldoi: https://doi.org/10.1112/jlms.12975
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isi: 1
issue: '3'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: Wiley
quality_controlled: '1'
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status: public
supplementarymaterial: no
title: Special cubic zeros and the dual variety
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type: journal_article
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year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '17323'
abstract:
- lang: eng
text: We investigate strong divisibility sequences and produce lower and upper bounds
for the density of integers in the sequence that only have (somewhat) large prime
factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility
sequences, discussing the limitations of our methods. At the end of the paper,
there is an appendix by Sandro Bettin on divisor closed sets that we use to study
the density of prime terms that appear in strong divisibility sequences.
acknowledgement: The authors are very grateful to Andrew Granville, Dimitris Koukoulopoulos,
Davide Lombardo,Florian Luca, Igor Shparlinski and Joni Teräväinen for useful comments.
While working on thispaper, the first author was supported by a FWF Grant (DOI 10.55776/P36278)
and the secondauthor was supported by the European Union’s Horizon 2020 research
and innovation programunder the Marie Skłodowska-Curie Grant Agreement Number 101034413.
article_number: e12269
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: Browning TD, Verzobio M. Strong divisibility sequences and sieve methods. Mathematika.
2024;70(4). doi:10.1112/mtk.12269
apa: Browning, T. D., & Verzobio, M. (2024). Strong divisibility sequences and
sieve methods. Mathematika. London Mathematical Society. https://doi.org/10.1112/mtk.12269
chicago: Browning, Timothy D, and Matteo Verzobio. “Strong Divisibility Sequences
and Sieve Methods.” Mathematika. London Mathematical Society, 2024. https://doi.org/10.1112/mtk.12269.
ieee: T. D. Browning and M. Verzobio, “Strong divisibility sequences and sieve methods,”
Mathematika, vol. 70, no. 4. London Mathematical Society, 2024.
ista: Browning TD, Verzobio M. 2024. Strong divisibility sequences and sieve methods.
Mathematika. 70(4), e12269.
mla: Browning, Timothy D., and Matteo Verzobio. “Strong Divisibility Sequences and
Sieve Methods.” Mathematika, vol. 70, no. 4, e12269, London Mathematical
Society, 2024, doi:10.1112/mtk.12269.
short: T.D. Browning, M. Verzobio, Mathematika 70 (2024).
corr_author: '1'
das_tickbox: '0'
date_created: 2024-07-28T22:01:08Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-07-29T10:01:24Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1112/mtk.12269
ec_funded: 1
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isi: 1
issue: '4'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Mathematika
publication_identifier:
eissn:
- 2041-7942
issn:
- 0025-5793
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
researchdata_availability: no
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status: public
supplementarymaterial: no
title: Strong divisibility sequences and sieve methods
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short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 70
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18064'
abstract:
- lang: eng
text: " We show that the total number of non-torsion integral points on the elliptic
curves ED : y\r\n2 = x3 − D2x, where D ranges over positive squarefree integers
less than N, is O(N(log N)\r\n−1/4+ǫ). The proof involves a discriminant-lowering
procedure on integral binary quartic forms and an application of Heath-Brown’s
method on estimating the average size of the 2-Selmer group of the curves in this
family."
article_number: '109946'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Yik Tung
full_name: Chan, Yik Tung
id: c4c0afc8-9262-11ed-9231-d8b0bc743af1
last_name: Chan
orcid: 0000-0001-8467-4106
citation:
ama: Chan S. The average number of integral points on the congruent number curves.
Advances in Mathematics. 2024;457(11). doi:10.1016/j.aim.2024.109946
apa: Chan, S. (2024). The average number of integral points on the congruent number
curves. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2024.109946
chicago: Chan, Stephanie. “The Average Number of Integral Points on the Congruent
Number Curves.” Advances in Mathematics. Elsevier, 2024. https://doi.org/10.1016/j.aim.2024.109946.
ieee: S. Chan, “The average number of integral points on the congruent number curves,”
Advances in Mathematics, vol. 457, no. 11. Elsevier, 2024.
ista: Chan S. 2024. The average number of integral points on the congruent number
curves. Advances in Mathematics. 457(11), 109946.
mla: Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number
Curves.” Advances in Mathematics, vol. 457, no. 11, 109946, Elsevier, 2024,
doi:10.1016/j.aim.2024.109946.
short: S. Chan, Advances in Mathematics 457 (2024).
corr_author: '1'
das_tickbox: '0'
date_created: 2024-09-15T22:01:39Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2026-07-29T10:03:09Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1016/j.aim.2024.109946
external_id:
arxiv:
- '2112.01615'
file:
- access_level: open_access
checksum: f555742540ad91a3040aeafd68b1fcde
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month: '11'
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oa_version: Published Version
publication: Advances in Mathematics
publication_identifier:
eissn:
- 1090-2082
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
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status: public
supplementarymaterial: no
title: The average number of integral points on the congruent number curves
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name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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volume: 457
year: '2024'
...
---
_id: '18173'
abstract:
- lang: eng
text: Using a two-dimensional version of the delta method, we establish an asymptotic
formula for the number of rational points of bounded height on non-singular complete
intersections of cubic and quadric hypersurfaces of dimension at least 23 over
Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation.
acknowledgement: The author would like to thank his supervisor Tim Browning for suggesting
this project and many helpful conversations and Pankaj Vishe for useful comments.
Moreover, he is grateful to Dante Bonolis and Julian Lyczak for sharing their expertise
in exponential sums and geometry. While working on this paper, the author was supported
by FWF grant (DOI 10.55776/P36278).
article_number: e12991
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jakob
full_name: Glas, Jakob
id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
last_name: Glas
citation:
ama: Glas J. Rational points on complete intersections of cubic and quadric hypersurfaces
over Fq(t). Journal of the London Mathematical Society. 2024;110(4). doi:10.1112/jlms.12991
apa: Glas, J. (2024). Rational points on complete intersections of cubic and quadric
hypersurfaces over Fq(t). Journal of the London Mathematical Society. London
Mathematical Society. https://doi.org/10.1112/jlms.12991
chicago: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric
Hypersurfaces over Fq(T).” Journal of the London Mathematical Society.
London Mathematical Society, 2024. https://doi.org/10.1112/jlms.12991.
ieee: J. Glas, “Rational points on complete intersections of cubic and quadric hypersurfaces
over Fq(t),” Journal of the London Mathematical Society, vol. 110, no.
4. London Mathematical Society, 2024.
ista: Glas J. 2024. Rational points on complete intersections of cubic and quadric
hypersurfaces over Fq(t). Journal of the London Mathematical Society. 110(4),
e12991.
mla: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric
Hypersurfaces over Fq(T).” Journal of the London Mathematical Society,
vol. 110, no. 4, e12991, London Mathematical Society, 2024, doi:10.1112/jlms.12991.
short: J. Glas, Journal of the London Mathematical Society 110 (2024).
corr_author: '1'
das_tickbox: '0'
date_created: 2024-10-06T22:01:11Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-07-29T10:04:55Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1112/jlms.12991
external_id:
arxiv:
- '2306.02718'
file:
- access_level: open_access
checksum: 11ebf690363151026ce81f91f2220855
content_type: application/pdf
creator: dernst
date_created: 2024-10-07T08:51:01Z
date_updated: 2024-10-07T08:51:01Z
file_id: '18181'
file_name: 2024_JLondonMathSoc_Glas.pdf
file_size: 579601
relation: main_file
success: 1
file_date_updated: 2024-10-07T08:51:01Z
fulldoi: https://doi.org/10.1112/jlms.12991
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intvolume: ' 110'
issue: '4'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
related_material:
record:
- id: '18132'
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researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Rational points on complete intersections of cubic and quadric hypersurfaces
over Fq(t)
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 110
year: '2024'
...
---
OA_place: repository
_id: '18295'
abstract:
- lang: eng
text: By developing a suitable version of the circle method, we show that the space
of degree e rational curves on a smooth hypersurface of degree d has only canonical
singularities provided its dimension is sufficiently large with respect to e and
d.
article_processing_charge: No
arxiv: 1
author:
- first_name: Jakob
full_name: Glas, Jakob
id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
last_name: Glas
citation:
ama: Glas J. Canonical singularities on moduli spaces of rational curves via the
circle method. arXiv. doi:10.48550/arXiv.2405.16648
apa: Glas, J. (n.d.). Canonical singularities on moduli spaces of rational curves
via the circle method. arXiv. https://doi.org/10.48550/arXiv.2405.16648
chicago: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves
via the Circle Method.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2405.16648.
ieee: J. Glas, “Canonical singularities on moduli spaces of rational curves via
the circle method,” arXiv. .
ista: Glas J. Canonical singularities on moduli spaces of rational curves via the
circle method. arXiv, 10.48550/arXiv.2405.16648.
mla: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via
the Circle Method.” ArXiv, doi:10.48550/arXiv.2405.16648.
short: J. Glas, ArXiv (n.d.).
corr_author: '1'
das_tickbox: '0'
date_created: 2024-10-10T13:15:43Z
date_published: 2024-05-26T00:00:00Z
date_updated: 2026-07-29T10:05:58Z
day: '26'
department:
- _id: TiBr
doi: 10.48550/arXiv.2405.16648
external_id:
arxiv:
- '2405.16648'
fulldoi: https://doi.org/10.48550/arXiv.2405.16648
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2405.16648
month: '05'
oa: 1
oa_version: Preprint
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '19013'
relation: later_version
status: public
- id: '18132'
relation: dissertation_contains
status: public
researchdata_availability: no
status: public
supplementarymaterial: no
title: Canonical singularities on moduli spaces of rational curves via the circle
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: preprint
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...
---
OA_place: repository
_id: '19013'
abstract:
- lang: eng
text: We study the singularities of the moduli space of degree e maps from smooth
genus g curves to an arbitrary smooth hypersurface of low degree. For e large
compared to g, we show that these moduli spaces have at worst terminal singularities.
Our main approach is to study the jet schemes of these moduli spaces by developing
a suitable form of the circle method.
article_processing_charge: No
arxiv: 1
author:
- first_name: Jakob
full_name: Glas, Jakob
id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
last_name: Glas
- first_name: 'Matthew '
full_name: 'Hase-Liu, Matthew '
last_name: Hase-Liu
citation:
ama: Glas J, Hase-Liu M. Terminal singularities of the moduli space of curves on
low degree hypersurfaces and the circle method. arXiv. doi:10.48550/arXiv.2412.14923
apa: Glas, J., & Hase-Liu, M. (n.d.). Terminal singularities of the moduli space
of curves on low degree hypersurfaces and the circle method. arXiv. https://doi.org/10.48550/arXiv.2412.14923
chicago: Glas, Jakob, and Matthew Hase-Liu. “Terminal Singularities of the Moduli
Space of Curves on Low Degree Hypersurfaces and the Circle Method.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2412.14923.
ieee: J. Glas and M. Hase-Liu, “Terminal singularities of the moduli space of curves
on low degree hypersurfaces and the circle method,” arXiv. .
ista: Glas J, Hase-Liu M. Terminal singularities of the moduli space of curves on
low degree hypersurfaces and the circle method. arXiv, 10.48550/arXiv.2412.14923.
mla: Glas, Jakob, and Matthew Hase-Liu. “Terminal Singularities of the Moduli Space
of Curves on Low Degree Hypersurfaces and the Circle Method.” ArXiv, doi:10.48550/arXiv.2412.14923.
short: J. Glas, M. Hase-Liu, ArXiv (n.d.).
corr_author: '1'
das_tickbox: '0'
date_created: 2025-02-07T12:04:11Z
date_published: 2024-12-19T00:00:00Z
date_updated: 2026-07-29T10:05:58Z
day: '19'
department:
- _id: TiBr
doi: 10.48550/arXiv.2412.14923
external_id:
arxiv:
- '2412.14923'
fulldoi: https://doi.org/10.48550/arXiv.2412.14923
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2412.14923
month: '12'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '18295'
relation: earlier_version
status: public
researchdata_availability: no
status: public
supplementarymaterial: no
title: Terminal singularities of the moduli space of curves on low degree hypersurfaces
and the circle 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: preprint
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '20071'
abstract:
- lang: eng
text: Farkas established that a system of linear inequalities has a solution if
and only if we cannot obtain a contradiction by taking a linear combination of
the inequalities. We state and formally prove several Farkas-like theorems over
linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the
case when some coefficients are allowed to take "infinite values".
acknowledgement: We would like to thank David Bartl and Jasmin Blanchette for frequent
consultations. We would also like to express gratitude to Andrew Yang for the proof
of Finset.univ sum of zero when not and to Henrik B¨oving for a help with generalization
from extended rationals to extended linearly ordered fields. We would also like
to acknowledge Antoine Chambert-Loir, Apurva Nakade, Ya¨el Dillies, Richard Copley,
Edward van de Meent, Markus Himmel, Mario Carneiro, and Kevin Buzzard.
article_number: '2409.08119'
article_processing_charge: No
arxiv: 1
author:
- first_name: Martin
full_name: Dvorak, Martin
id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425
last_name: Dvorak
orcid: 0000-0001-5293-214X
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: Dvorak M, Kolmogorov V. Duality theory in linear optimization and its extensions
-- formally verified. arXiv. doi:10.48550/arXiv.2409.08119
apa: Dvorak, M., & Kolmogorov, V. (n.d.). Duality theory in linear optimization
and its extensions -- formally verified. arXiv. https://doi.org/10.48550/arXiv.2409.08119
chicago: Dvorak, Martin, and Vladimir Kolmogorov. “Duality Theory in Linear Optimization
and Its Extensions -- Formally Verified.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.08119.
ieee: M. Dvorak and V. Kolmogorov, “Duality theory in linear optimization and its
extensions -- formally verified,” arXiv. .
ista: Dvorak M, Kolmogorov V. Duality theory in linear optimization and its extensions
-- formally verified. arXiv, 2409.08119.
mla: Dvorak, Martin, and Vladimir Kolmogorov. “Duality Theory in Linear Optimization
and Its Extensions -- Formally Verified.” ArXiv, 2409.08119, doi:10.48550/arXiv.2409.08119.
short: M. Dvorak, V. Kolmogorov, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-07-23T11:21:52Z
date_published: 2024-09-12T00:00:00Z
date_updated: 2026-07-29T12:56:51Z
day: '12'
department:
- _id: GradSch
- _id: VlKo
doi: 10.48550/arXiv.2409.08119
external_id:
arxiv:
- '2409.08119'
fulldoi: https://doi.org/10.48550/arXiv.2409.08119
keyword:
- Farkas lemma
- linear programming
- extended reals
- calculus of inductive constructions
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2409.08119
month: '09'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
link:
- description: full version of all definitions, statement, and proofs
relation: software
url: https://github.com/madvorak/duality/tree/v3.2
record:
- id: '22607'
relation: later_version
status: public
- id: '21393'
relation: dissertation_contains
status: public
status: public
title: Duality theory in linear optimization and its extensions -- formally verified
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18307'
abstract:
- lang: eng
text: Vaccination is the most effective tool to control infectious diseases. However,
the evolution of vaccine resistance, exemplified by vaccine resistance in SARS-CoV-2,
remains a concern. Here, we model complex vaccination strategies against a pathogen
with multiple epitopes—molecules targeted by the vaccine. We found that a vaccine
targeting one epitope was ineffective in preventing vaccine escape. Vaccine resistance
in highly infectious pathogens was prevented by the full-epitope vaccine, that
is, one targeting all available epitopes, but only when the rate of pathogen evolution
was low. Strikingly, a bet-hedging strategy of random administration of vaccines
targeting different epitopes was the most effective in preventing vaccine resistance
in pathogens with the low rate of infection and high rate of evolution. Thus,
complex vaccination strategies, when biologically feasible, may be preferable
to the currently used single-vaccine approaches for long-term control of disease
outbreaks, especially when applied to livestock with near 100% vaccination rates.
acknowledgement: We thank Raimundo Julian Saona Urmeneta, Maike Morrison, Sergey Kryazhimskiy,
Hiroki Ishikawa, Simone Pigolotti, and Shingo Miyauchi for fruitful discussions.
We also thank the participants of the FRISBI seminar at ISTA for useful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Simon
full_name: Rella, Simon
id: B4765ACA-AA38-11E9-AC9A-0930E6697425
last_name: Rella
- first_name: Yuliya A.
full_name: Kulikova, Yuliya A.
last_name: Kulikova
- first_name: Aygul
full_name: Minnegalieva, Aygul
id: 87DF77F0-1D9A-11EA-B6AE-CE443DDC885E
last_name: Minnegalieva
- first_name: Fyodor
full_name: Kondrashov, Fyodor
id: 44FDEF62-F248-11E8-B48F-1D18A9856A87
last_name: Kondrashov
orcid: 0000-0001-8243-4694
citation:
ama: 'Rella S, Kulikova YA, Minnegalieva A, Kondrashov F. Complex vaccination strategies
prevent the emergence of vaccine resistance. Evolution: International journal
of organic evolution. 2024;78(10):1722-1738. doi:10.1093/evolut/qpae106'
apa: 'Rella, S., Kulikova, Y. A., Minnegalieva, A., & Kondrashov, F. (2024).
Complex vaccination strategies prevent the emergence of vaccine resistance. Evolution:
International Journal of Organic Evolution. Oxford University Press. https://doi.org/10.1093/evolut/qpae106'
chicago: 'Rella, Simon, Yuliya A. Kulikova, Aygul Minnegalieva, and Fyodor Kondrashov.
“Complex Vaccination Strategies Prevent the Emergence of Vaccine Resistance.”
Evolution: International Journal of Organic Evolution. Oxford University
Press, 2024. https://doi.org/10.1093/evolut/qpae106.'
ieee: 'S. Rella, Y. A. Kulikova, A. Minnegalieva, and F. Kondrashov, “Complex vaccination
strategies prevent the emergence of vaccine resistance,” Evolution: International
journal of organic evolution, vol. 78, no. 10. Oxford University Press, pp.
1722–1738, 2024.'
ista: 'Rella S, Kulikova YA, Minnegalieva A, Kondrashov F. 2024. Complex vaccination
strategies prevent the emergence of vaccine resistance. Evolution: International
journal of organic evolution. 78(10), 1722–1738.'
mla: 'Rella, Simon, et al. “Complex Vaccination Strategies Prevent the Emergence
of Vaccine Resistance.” Evolution: International Journal of Organic Evolution,
vol. 78, no. 10, Oxford University Press, 2024, pp. 1722–38, doi:10.1093/evolut/qpae106.'
short: 'S. Rella, Y.A. Kulikova, A. Minnegalieva, F. Kondrashov, Evolution: International
Journal of Organic Evolution 78 (2024) 1722–1738.'
corr_author: '1'
date_created: 2024-10-13T22:01:50Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-07-29T12:57:48Z
day: '01'
ddc:
- '570'
department:
- _id: GaTk
doi: 10.1093/evolut/qpae106
external_id:
isi:
- '001286581900001'
pmid:
- '38990788'
file:
- access_level: open_access
checksum: 5c6e8475bb88b07d424a5130d5e91e74
content_type: application/pdf
creator: dernst
date_created: 2024-10-21T09:34:50Z
date_updated: 2024-10-21T09:34:50Z
file_id: '18453'
file_name: 2024_Evolution_Rella.pdf
file_size: 29360811
relation: main_file
success: 1
file_date_updated: 2024-10-21T09:34:50Z
fulldoi: https://doi.org/10.1093/evolut/qpae106
has_accepted_license: '1'
intvolume: ' 78'
isi: 1
issue: '10'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1722-1738
pmid: 1
publication: 'Evolution: International journal of organic evolution'
publication_identifier:
eissn:
- 1558-5646
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/Simon-Re/complex-vaccination
record:
- id: '14862'
relation: research_data
status: public
- id: '20811'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Complex vaccination strategies prevent the emergence of vaccine resistance
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 78
year: '2024'
...
---
_id: '15168'
abstract:
- lang: eng
text: 'A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its
vertices with colours 1, … , k such that each edge contains a unique maximal colour.
Deciding whether an input hypergraph admits LO k-colouring with a fixed number
of colours is NP-complete (and in the special case of graphs, LO colouring coincides
with the usual graph colouring). Here, we investigate the complexity of approximating
the "linearly ordered chromatic number" of a hypergraph. We prove that the following
promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between
the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable.
We prove this result by a combination of algebraic, topological, and combinatorial
methods, building on and extending a topological approach for studying approximate
graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).'
acknowledgement: "Marek Filakovský: This research was supported by Charles University
(project PRIMUS/\r\n21/SCI/014), the Austrian Science Fund (FWF project P31312-N35),
and MSCAfellow5_MUNI\r\n(CZ.02.01.01/00/22_010/0003229). Tamio-Vesa Nakajima: This
research was funded by UKRI EP/X024431/1 and by a Clarendon Fund Scholarship. All
data is provided in full in the results section of this paper. Jakub Opršal: This
project has received funding from the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413.
Uli Wagner: This research was supported by the Austrian Science Fund (FWF project
P31312-N35)."
alternative_title:
- LIPIcs
article_number: '34'
article_processing_charge: No
arxiv: 1
author:
- first_name: Marek
full_name: Filakovský, Marek
id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87
last_name: Filakovský
- first_name: Tamio Vesa
full_name: Nakajima, Tamio Vesa
last_name: Nakajima
- first_name: Jakub
full_name: Opršal, Jakub
id: ec596741-c539-11ec-b829-c79322a91242
last_name: Opršal
orcid: 0000-0003-1245-3456
- first_name: Gianluca
full_name: Tasinato, Gianluca
id: 0433290C-AF8F-11E9-A4C7-F729E6697425
last_name: Tasinato
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. Hardness of linearly
ordered 4-colouring of 3-colourable 3-uniform hypergraphs. In: 41st International
Symposium on Theoretical Aspects of Computer Science. Vol 289. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.STACS.2024.34'
apa: 'Filakovský, M., Nakajima, T. V., Opršal, J., Tasinato, G., & Wagner, U.
(2024). Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs.
In 41st International Symposium on Theoretical Aspects of Computer Science
(Vol. 289). Clermont-Ferrand, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.STACS.2024.34'
chicago: Filakovský, Marek, Tamio Vesa Nakajima, Jakub Opršal, Gianluca Tasinato,
and Uli Wagner. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform
Hypergraphs.” In 41st International Symposium on Theoretical Aspects of Computer
Science, Vol. 289. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
https://doi.org/10.4230/LIPIcs.STACS.2024.34.
ieee: M. Filakovský, T. V. Nakajima, J. Opršal, G. Tasinato, and U. Wagner, “Hardness
of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs,” in 41st
International Symposium on Theoretical Aspects of Computer Science, Clermont-Ferrand,
France, 2024, vol. 289.
ista: 'Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. 2024. Hardness
of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. 41st International
Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical
Aspects of Computer Science, LIPIcs, vol. 289, 34.'
mla: Filakovský, Marek, et al. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable
3-Uniform Hypergraphs.” 41st International Symposium on Theoretical Aspects
of Computer Science, vol. 289, 34, Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, 2024, doi:10.4230/LIPIcs.STACS.2024.34.
short: M. Filakovský, T.V. Nakajima, J. Opršal, G. Tasinato, U. Wagner, in:, 41st
International Symposium on Theoretical Aspects of Computer Science, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2024.
conference:
end_date: 2024-03-14
location: Clermont-Ferrand, France
name: 'STACS: Symposium on Theoretical Aspects of Computer Science'
start_date: 2024-03-12
corr_author: '1'
date_created: 2024-03-24T23:00:59Z
date_published: 2024-03-01T00:00:00Z
date_updated: 2026-07-29T13:13:17Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.STACS.2024.34
ec_funded: 1
external_id:
arxiv:
- '2312.12981'
isi:
- '001300393400034'
file:
- access_level: open_access
checksum: 0524d4189fd1ed08989546511343edf3
content_type: application/pdf
creator: dernst
date_created: 2024-03-25T07:44:30Z
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fulldoi: https://doi.org/10.4230/LIPIcs.STACS.2024.34
has_accepted_license: '1'
intvolume: ' 289'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
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call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: 41st International Symposium on Theoretical Aspects of Computer Science
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959773119'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
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scopus_import: '1'
status: public
title: Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs
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: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 289
year: '2024'
...
---
OA_place: repository
_id: '19545'
abstract:
- lang: eng
text: "We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly
in the entire spectrum, in particular near the spectral edges, with a\r\nbound
on the fluctuation that is optimal for any observable. This complements\r\nearlier
works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma
10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142)
that were restricted either to the bulk of the spectrum or to\r\nspecial observables.
As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally
accounts for the edge scaling."
acknowledgement: Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.
article_processing_charge: No
arxiv: 1
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: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
citation:
ama: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for
Wigner matrices. arXiv. doi:10.48550/arXiv.2309.05488
apa: Cipolloni, G., Erdös, L., & Henheik, S. J. (n.d.). Eigenstate thermalisation
at the edge for Wigner matrices. arXiv. https://doi.org/10.48550/arXiv.2309.05488
chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate
Thermalisation at the Edge for Wigner Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.05488.
ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the
edge for Wigner matrices,” arXiv. .
ista: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for
Wigner matrices. arXiv, 10.48550/arXiv.2309.05488.
mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner
Matrices.” ArXiv, doi:10.48550/arXiv.2309.05488.
short: G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T08:19:22Z
date_published: 2024-12-17T00:00:00Z
date_updated: 2026-07-29T13:18:16Z
day: '17'
department:
- _id: LaEr
doi: 10.48550/arXiv.2309.05488
ec_funded: 1
external_id:
arxiv:
- '2309.05488'
fulldoi: https://doi.org/10.48550/arXiv.2309.05488
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2309.05488
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: arXiv
publication_status: draft
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
status: public
title: Eigenstate thermalisation at the edge 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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: repository
_id: '19550'
abstract:
- lang: eng
text: "We introduce a multi-band BCS free energy functional and prove that for a\r\nmulti-band
superconductor the effect of inter-band coupling can only increase\r\nthe critical
temperature, irrespective of its attractive or repulsive nature\r\nand its strength.
Further, for weak coupling and weaker inter-band coupling, we\r\nprove that the
dependence of the increase in critical temperature on the\r\ninter-band coupling
is (1) linear, if there are two or more equally strongly\r\nsuperconducting bands,
or (2) quadratic, if there is only one dominating band."
article_processing_charge: No
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: Edwin
full_name: Langmann, Edwin
last_name: Langmann
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced
critical temperatures. arXiv. doi:10.48550/arXiv.2409.17297
apa: Henheik, S. J., Langmann, E., & Lauritsen, A. B. (n.d.). Multi-band superconductors
have enhanced critical temperatures. arXiv. https://doi.org/10.48550/arXiv.2409.17297
chicago: Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band
Superconductors Have Enhanced Critical Temperatures.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.17297.
ieee: S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors
have enhanced critical temperatures,” arXiv. .
ista: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced
critical temperatures. arXiv, 10.48550/arXiv.2409.17297.
mla: Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical
Temperatures.” ArXiv, doi:10.48550/arXiv.2409.17297.
short: S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T11:43:58Z
date_published: 2024-10-21T00:00:00Z
date_updated: 2026-07-29T13:18:16Z
day: '21'
department:
- _id: LaEr
- _id: RoSe
doi: 10.48550/arXiv.2409.17297
external_id:
arxiv:
- '2409.17297'
fulldoi: https://doi.org/10.48550/arXiv.2409.17297
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2409.17297
month: '10'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '22290'
relation: later_version
status: public
- id: '19540'
relation: dissertation_contains
status: public
status: public
title: Multi-band superconductors have enhanced critical temperatures
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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '17049'
abstract:
- lang: eng
text: We consider large non-Hermitian NxN matrices with an additive independent,
identically distributed (i.i.d.) noise for each matrix elements. We show that
already a small noise of variance 1/N completely thermalises the bulk singular
vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity
(QUE) with an optimal speed of convergence. In physics terms, we thus extend the
Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and
proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an
i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal
overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also
known as the (square of the) eigenvalue condition number measuring the sensitivity
of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment
beyond the explicitly computable Ginibre ensemble apart from the very recent upper
bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition
of general observables in random matrix theory that governs the size of products
of resolvents with deterministic matrices in between.
acknowledgement: "Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported
by the SNSF Ambizione Grant PZ00P2_209089."
article_number: '110495'
article_processing_charge: Yes (via OA deal)
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: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- 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, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector
overlaps for non-Hermitian random matrices. Journal of Functional Analysis.
2024;287(4). doi:10.1016/j.jfa.2024.110495
apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Schröder, D. J. (2024). Optimal
lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal
of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110495
chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder.
“Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.”
Journal of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110495.
ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower
bound on eigenvector overlaps for non-Hermitian random matrices,” Journal of
Functional Analysis, vol. 287, no. 4. Elsevier, 2024.
ista: Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on
eigenvector overlaps for non-Hermitian random matrices. Journal of Functional
Analysis. 287(4), 110495.
mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for
Non-Hermitian Random Matrices.” Journal of Functional Analysis, vol. 287,
no. 4, 110495, Elsevier, 2024, doi:10.1016/j.jfa.2024.110495.
short: G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional
Analysis 287 (2024).
corr_author: '1'
date_created: 2024-05-26T22:00:57Z
date_published: 2024-08-15T00:00:00Z
date_updated: 2026-07-29T13:18:17Z
day: '15'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2024.110495
ec_funded: 1
external_id:
isi:
- '001325502400001'
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intvolume: ' 287'
isi: 1
issue: '4'
language:
- iso: eng
month: '08'
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: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
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relation: dissertation_contains
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scopus_import: '1'
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title: Optimal lower bound on eigenvector overlaps for non-Hermitian random 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 287
year: '2024'
...