---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '14278'
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 almost every ellipse
that preserves integrability near the boundary, is itself an ellipse. We apply
this result to study local spectral uniqueness of ellipses using the connection
between the wave trace of the Laplacian and the dynamics near the boundary and
establish local uniqueness for almost all of them.'
acknowledgement: 'The author acknowledges the partial support of the European Research
Council Grant #885707. He also thanks Vadim Kaloshin for proposing the idea of the
project and greatly aiding the implementation. The author is also grateful to Hamid
Hezari, Amir Vig, Steve Zelditch, Comlan E. Koudjinan, Corentin Fierobe, Ngo Nhok
Tkhai Shon and Roman Sarapin for useful discussions. The author also acknowledges
partial support of ISTern summer program. The project started in the summer of 2021,
when the author was an intern at ISTA. Open access funding provided by Institute
of Science and Technology (IST Austria).'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Illya
full_name: Koval, Illya
id: 2eed1f3b-896a-11ed-bdf8-93c7c4bf159e
last_name: Koval
citation:
ama: Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost
every ellipse. Inventiones Mathematicae. 2026;244:221-298. doi:10.1007/s00222-025-01397-y
apa: Koval, I. (2026). Local strong Birkhoff conjecture and local spectral rigidity
of almost every ellipse. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-025-01397-y
chicago: Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity
of Almost Every Ellipse.” Inventiones Mathematicae. Springer Nature, 2026.
https://doi.org/10.1007/s00222-025-01397-y.
ieee: I. Koval, “Local strong Birkhoff conjecture and local spectral rigidity of
almost every ellipse,” Inventiones Mathematicae, vol. 244. Springer Nature,
pp. 221–298, 2026.
ista: Koval I. 2026. Local strong Birkhoff conjecture and local spectral rigidity
of almost every ellipse. Inventiones Mathematicae. 244, 221–298.
mla: Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity
of Almost Every Ellipse.” Inventiones Mathematicae, vol. 244, Springer
Nature, 2026, pp. 221–98, doi:10.1007/s00222-025-01397-y.
short: I. Koval, Inventiones Mathematicae 244 (2026) 221–298.
corr_author: '1'
das_tickbox: '0'
date_created: 2023-09-06T08:35:43Z
date_published: 2026-04-01T00:00:00Z
date_updated: 2026-07-23T10:58:59Z
day: '01'
ddc:
- '510'
department:
- _id: GradSch
- _id: VaKa
doi: 10.1007/s00222-025-01397-y
ec_funded: 1
external_id:
arxiv:
- '2111.12171'
file:
- access_level: open_access
checksum: 487fa9113e1bbf32a6c70e6d1e8f63bc
content_type: application/pdf
creator: dernst
date_created: 2026-07-23T10:55:24Z
date_updated: 2026-07-23T10:55:24Z
file_id: '22394'
file_name: 2026_InventionesMath_Koval.pdf
file_size: 2256345
relation: main_file
success: 1
file_date_updated: 2026-07-23T10:55:24Z
has_accepted_license: '1'
intvolume: ' 244'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
mathsc:
- 37C83
- 35J05
- 37J70
- 74J25
month: '04'
oa: 1
oa_version: Published Version
page: 221-298
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Local strong Birkhoff conjecture and local spectral rigidity of almost every
ellipse
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: 244
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '20838'
abstract:
- lang: eng
text: "For any 1 ≤ r ≤ ∞, we show that every diffeomorphism of a manifold of the
form\r\nR/Z × M is a total renormalization of a Cr-close to identity map. In other
words, for\r\nevery diffeomorphism f of R/Z×M, there exists a map g arbitrarily
close to identity\r\nsuch that the first return map of g to a domain is conjugate
to f and moreover the\r\norbit of this domain is equal to R/Z×M. This enables
us to localize near the identity\r\nthe existence of many properties in dynamical
systems, such as being Bernoulli for a\r\nsmooth volume form."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Pierre
full_name: Berger, Pierre
last_name: Berger
- first_name: Nicolaz
full_name: Gourmelon, Nicolaz
last_name: Gourmelon
- first_name: Mathieu
full_name: Helfter, Mathieu
id: 7d296fbe-e2c6-11ee-84d3-d5c2945f9a57
last_name: Helfter
citation:
ama: Berger P, Gourmelon N, Helfter M. Every diffeomorphism is a total renormalization
of a close to identity map. Inventiones mathematicae. 2024;239(2):431-468.
doi:10.1007/s00222-024-01305-w
apa: Berger, P., Gourmelon, N., & Helfter, M. (2024). Every diffeomorphism is
a total renormalization of a close to identity map. Inventiones Mathematicae.
Springer Nature. https://doi.org/10.1007/s00222-024-01305-w
chicago: Berger, Pierre, Nicolaz Gourmelon, and Mathieu Helfter. “Every Diffeomorphism
Is a Total Renormalization of a Close to Identity Map.” Inventiones Mathematicae.
Springer Nature, 2024. https://doi.org/10.1007/s00222-024-01305-w.
ieee: P. Berger, N. Gourmelon, and M. Helfter, “Every diffeomorphism is a total
renormalization of a close to identity map,” Inventiones mathematicae,
vol. 239, no. 2. Springer Nature, pp. 431–468, 2024.
ista: Berger P, Gourmelon N, Helfter M. 2024. Every diffeomorphism is a total renormalization
of a close to identity map. Inventiones mathematicae. 239(2), 431–468.
mla: Berger, Pierre, et al. “Every Diffeomorphism Is a Total Renormalization of
a Close to Identity Map.” Inventiones Mathematicae, vol. 239, no. 2, Springer
Nature, 2024, pp. 431–68, doi:10.1007/s00222-024-01305-w.
short: P. Berger, N. Gourmelon, M. Helfter, Inventiones Mathematicae 239 (2024)
431–468.
date_created: 2025-12-19T10:15:13Z
date_published: 2024-12-19T00:00:00Z
date_updated: 2025-12-29T12:03:10Z
day: '19'
doi: 10.1007/s00222-024-01305-w
extern: '1'
external_id:
arxiv:
- '2210.09064'
intvolume: ' 239'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2210.09064
month: '12'
oa: 1
oa_version: Preprint
page: 431-468
publication: Inventiones mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Every diffeomorphism is a total renormalization of a close to identity map
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 239
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '22065'
abstract:
- lang: eng
text: The Benjamin–Ono equation is shown to be well-posed, both on the line and
on the circle, in the Sobolev spaces H^s for s > -1/2. The proof rests on a new
gauge transformation and benefits from our introduction of a modified Lax pair
representation of the full hierarchy. As we will show, these developments yield
important additional dividends beyond well-posedness, including (i) the unification
of the diverse approaches to polynomial conservation laws; (ii) a generalization
of Gérard’s explicit formula to the full hierarchy; and (iii) new virial-type
identities covering all equations in the hierarchy.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
full_name: Killip, Rowan
last_name: Killip
- first_name: Thierry
full_name: Laurens, Thierry
last_name: Laurens
- first_name: Monica
full_name: Visan, Monica
id: 056daca0-b8d1-11f0-964f-f91054abf8ca
last_name: Visan
citation:
ama: Killip R, Laurens T, Vişan M. Sharp well-posedness for the Benjamin–Ono equation.
Inventiones mathematicae. 2024;236(3):999-1054. doi:10.1007/s00222-024-01250-8
apa: Killip, R., Laurens, T., & Vişan, M. (2024). Sharp well-posedness for the
Benjamin–Ono equation. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-024-01250-8
chicago: Killip, Rowan, Thierry Laurens, and Monica Vişan. “Sharp Well-Posedness
for the Benjamin–Ono Equation.” Inventiones Mathematicae. Springer Nature,
2024. https://doi.org/10.1007/s00222-024-01250-8.
ieee: R. Killip, T. Laurens, and M. Vişan, “Sharp well-posedness for the Benjamin–Ono
equation,” Inventiones mathematicae, vol. 236, no. 3. Springer Nature,
pp. 999–1054, 2024.
ista: Killip R, Laurens T, Vişan M. 2024. Sharp well-posedness for the Benjamin–Ono
equation. Inventiones mathematicae. 236(3), 999–1054.
mla: Killip, Rowan, et al. “Sharp Well-Posedness for the Benjamin–Ono Equation.”
Inventiones Mathematicae, vol. 236, no. 3, Springer Nature, 2024, pp. 999–1054,
doi:10.1007/s00222-024-01250-8.
short: R. Killip, T. Laurens, M. Vişan, Inventiones Mathematicae 236 (2024) 999–1054.
das_tickbox: '1'
date_created: 2026-06-19T08:13:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2026-06-30T07:11:40Z
day: '01'
doi: 10.1007/s00222-024-01250-8
extern: '1'
external_id:
arxiv:
- '2304.00124'
intvolume: ' 236'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2304.00124
month: '06'
oa: 1
oa_version: Preprint
page: 999-1054
publication: Inventiones mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sharp well-posedness for the Benjamin–Ono equation
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 236
year: '2024'
...
---
_id: '12877'
abstract:
- lang: eng
text: We consider billiards obtained by removing from the plane finitely many strictly
convex analytic obstacles satisfying the non-eclipse condition. The restriction
of the dynamics to the set of non-escaping orbits is conjugated to a subshift,
which provides a natural labeling of periodic orbits. We show that under suitable
symmetry and genericity assumptions, the Marked Length Spectrum determines the
geometry of the billiard table.
acknowledgement: 'J.D.S. and M.L. have been partially supported by the NSERC Discovery
grant, reference number 502617-2017. M.L. was also supported by the ERC project
692925 NUHGD of Sylvain Crovisier, by the ANR AAPG 2021 PRC CoSyDy: Conformally
symplectic dynamics, beyond symplectic dynamics (ANR-CE40-0014), and by the ANR
JCJC PADAWAN: Parabolic dynamics, bifurcations and wandering domains (ANR-21-CE40-0012).
V.K. acknowledges partial support of the NSF grant DMS-1402164 and ERC Grant # 885707.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Martin
full_name: Leguil, Martin
last_name: Leguil
citation:
ama: De Simoi J, Kaloshin V, Leguil M. Marked Length Spectral determination of analytic
chaotic billiards with axial symmetries. Inventiones Mathematicae. 2023;233:829-901.
doi:10.1007/s00222-023-01191-8
apa: De Simoi, J., Kaloshin, V., & Leguil, M. (2023). Marked Length Spectral
determination of analytic chaotic billiards with axial symmetries. Inventiones
Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-023-01191-8
chicago: De Simoi, Jacopo, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectral
Determination of Analytic Chaotic Billiards with Axial Symmetries.” Inventiones
Mathematicae. Springer Nature, 2023. https://doi.org/10.1007/s00222-023-01191-8.
ieee: J. De Simoi, V. Kaloshin, and M. Leguil, “Marked Length Spectral determination
of analytic chaotic billiards with axial symmetries,” Inventiones Mathematicae,
vol. 233. Springer Nature, pp. 829–901, 2023.
ista: De Simoi J, Kaloshin V, Leguil M. 2023. Marked Length Spectral determination
of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae.
233, 829–901.
mla: De Simoi, Jacopo, et al. “Marked Length Spectral Determination of Analytic
Chaotic Billiards with Axial Symmetries.” Inventiones Mathematicae, vol.
233, Springer Nature, 2023, pp. 829–901, doi:10.1007/s00222-023-01191-8.
short: J. De Simoi, V. Kaloshin, M. Leguil, Inventiones Mathematicae 233 (2023)
829–901.
date_created: 2023-04-30T22:01:05Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2025-04-14T07:53:46Z
day: '01'
department:
- _id: VaKa
doi: 10.1007/s00222-023-01191-8
ec_funded: 1
external_id:
arxiv:
- '1905.00890'
isi:
- '000978887600001'
intvolume: ' 233'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1905.00890
month: '08'
oa: 1
oa_version: Preprint
page: 829-901
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Marked Length Spectral determination of analytic chaotic billiards with axial
symmetries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 233
year: '2023'
...
---
_id: '10704'
abstract:
- lang: eng
text: We define and study the existence of very stable Higgs bundles on Riemann
surfaces, how it implies a precise formula for the multiplicity of the very stable
components of the global nilpotent cone and its relationship to mirror symmetry.
The main ingredients are the Bialynicki-Birula theory of C∗-actions on semiprojective
varieties, C∗ characters of indices of C∗-equivariant coherent sheaves, Hecke
transformation for Higgs bundles, relative Fourier–Mukai transform along the Hitchin
fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs
bundles.
acknowledgement: We would like to thank Brian Collier, Davide Gaiotto, Peter Gothen,
Jochen Heinloth, Daniel Huybrechts, Quoc Ho, Joel Kamnitzer, Gérard Laumon, Luca
Migliorini, Alexander Minets, Brent Pym, Peng Shan, Carlos Simpson, András Szenes,
Fernando R. Villegas, Richard Wentworth, Edward Witten and Kōta Yoshioka for interesting
comments and discussions. Most of all we are grateful for a long list of very helpful
comments by the referee. We would also like to thank the organizers of the Summer
School on Higgs bundles in Hamburg in September 2018, where the authors and Richard
Wentworth were giving lectures and where the work in this paper started by considering
the mirror of the Lagrangian upward flows W+E investigated in [17]. The second author
wishes to thank EPSRC and ICMAT for support. Open access funding provided by Institute
of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
- first_name: Nigel
full_name: Hitchin, Nigel
last_name: Hitchin
citation:
ama: Hausel T, Hitchin N. Very stable Higgs bundles, equivariant multiplicity and
mirror symmetry. Inventiones Mathematicae. 2022;228:893-989. doi:10.1007/s00222-021-01093-7
apa: Hausel, T., & Hitchin, N. (2022). Very stable Higgs bundles, equivariant
multiplicity and mirror symmetry. Inventiones Mathematicae. Springer Nature.
https://doi.org/10.1007/s00222-021-01093-7
chicago: Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant
Multiplicity and Mirror Symmetry.” Inventiones Mathematicae. Springer Nature,
2022. https://doi.org/10.1007/s00222-021-01093-7.
ieee: T. Hausel and N. Hitchin, “Very stable Higgs bundles, equivariant multiplicity
and mirror symmetry,” Inventiones Mathematicae, vol. 228. Springer Nature,
pp. 893–989, 2022.
ista: Hausel T, Hitchin N. 2022. Very stable Higgs bundles, equivariant multiplicity
and mirror symmetry. Inventiones Mathematicae. 228, 893–989.
mla: Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity
and Mirror Symmetry.” Inventiones Mathematicae, vol. 228, Springer Nature,
2022, pp. 893–989, doi:10.1007/s00222-021-01093-7.
short: T. Hausel, N. Hitchin, Inventiones Mathematicae 228 (2022) 893–989.
corr_author: '1'
date_created: 2022-01-30T23:01:34Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2025-04-15T06:53:08Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00222-021-01093-7
external_id:
arxiv:
- '2101.08583'
isi:
- '000745495400001'
file:
- access_level: open_access
checksum: a382ba75acebc9adfb8fe56247cb410e
content_type: application/pdf
creator: dernst
date_created: 2023-02-27T07:30:47Z
date_updated: 2023-02-27T07:30:47Z
file_id: '12687'
file_name: 2022_InventionesMahtematicae_Hausel.pdf
file_size: 1069538
relation: main_file
success: 1
file_date_updated: 2023-02-27T07:30:47Z
has_accepted_license: '1'
intvolume: ' 228'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 893-989
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- description: News on the ISTA Website
relation: press_release
url: https://ista.ac.at/en/news/the-tip-of-the-mathematical-iceberg/
scopus_import: '1'
status: public
title: Very stable Higgs bundles, equivariant multiplicity and mirror symmetry
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: 228
year: '2022'
...
---
_id: '7901'
abstract:
- lang: eng
text: We derive rigorously the leading order of the correlation energy of a Fermi
gas in a scaling regime of high density and weak interaction. The result verifies
the prediction of the random-phase approximation. Our proof refines the method
of collective bosonization in three dimensions. We approximately diagonalize an
effective Hamiltonian describing approximately bosonic collective excitations
around the Hartree–Fock state, while showing that gapless and non-collective excitations
have only a negligible effect on the ground state energy.
acknowledgement: We thank Christian Hainzl for helpful discussions and a referee for
very careful reading of the paper and many helpful suggestions. NB and RS were supported
by the European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (grant agreement No. 694227). Part of the research of NB
was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and
Peter Otte for explanations about the Luttinger model. PTN has received funding
from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under
Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901).
BS gratefully acknowledges financial support from the NCCR SwissMAP, from the Swiss
National Science Foundation through the Grant “Dynamical and energetic properties
of Bose-Einstein condensates” and from the European Research Council through the
ERC-AdG CLaQS (grant agreement No. 834782). All authors acknowledge support for
workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz
Association). NB, PTN, BS, and RS acknowledge support for workshop participation
from Fondation des Treilles.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Niels P
full_name: Benedikter, Niels P
id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
last_name: Benedikter
orcid: 0000-0002-1071-6091
- first_name: Phan Thành
full_name: Nam, Phan Thành
last_name: Nam
- first_name: Marcello
full_name: Porta, Marcello
last_name: Porta
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy
of a weakly interacting Fermi gas. Inventiones Mathematicae. 2021;225:885-979.
doi:10.1007/s00222-021-01041-5
apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R.
(2021). Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae.
Springer. https://doi.org/10.1007/s00222-021-01041-5
chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein,
and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.”
Inventiones Mathematicae. Springer, 2021. https://doi.org/10.1007/s00222-021-01041-5.
ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation
energy of a weakly interacting Fermi gas,” Inventiones Mathematicae, vol.
225. Springer, pp. 885–979, 2021.
ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation
energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979.
mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi
Gas.” Inventiones Mathematicae, vol. 225, Springer, 2021, pp. 885–979,
doi:10.1007/s00222-021-01041-5.
short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones
Mathematicae 225 (2021) 885–979.
date_created: 2020-05-28T16:48:20Z
date_published: 2021-05-03T00:00:00Z
date_updated: 2025-04-14T07:27:00Z
day: '03'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s00222-021-01041-5
ec_funded: 1
external_id:
arxiv:
- '2005.08933'
isi:
- '000646573600001'
file:
- access_level: open_access
checksum: f38c79dfd828cdc7f49a34b37b83d376
content_type: application/pdf
creator: dernst
date_created: 2022-05-16T12:23:40Z
date_updated: 2022-05-16T12:23:40Z
file_id: '11386'
file_name: 2021_InventMath_Benedikter.pdf
file_size: 1089319
relation: main_file
success: 1
file_date_updated: 2022-05-16T12:23:40Z
has_accepted_license: '1'
intvolume: ' 225'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 885-979
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Correlation energy of a weakly interacting Fermi gas
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: 225
year: '2021'
...
---
OA_place: repository
OA_type: green
_id: '22054'
abstract:
- lang: eng
text: We consider the Korteweg–de Vries equation with white noise initial data,
posed on the whole real line, and prove the almost sure existence of solutions.
Moreover, we show that the solutions obey the group property and follow a white
noise law at all times, past or future. As an offshoot of our methods, we also
obtain a new proof of the existence of solutions and the invariance of white noise
measure in the torus setting.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
full_name: Killip, Rowan
last_name: Killip
- first_name: Jason
full_name: Murphy, Jason
last_name: Murphy
- first_name: Monica
full_name: Visan, Monica
id: 056daca0-b8d1-11f0-964f-f91054abf8ca
last_name: Visan
citation:
ama: Killip R, Murphy J, Vişan M. Invariance of white noise for KdV on the line.
Inventiones mathematicae. 2020;222(1):203-282. doi:10.1007/s00222-020-00964-9
apa: Killip, R., Murphy, J., & Vişan, M. (2020). Invariance of white noise for
KdV on the line. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-020-00964-9
chicago: Killip, Rowan, Jason Murphy, and Monica Vişan. “Invariance of White Noise
for KdV on the Line.” Inventiones Mathematicae. Springer Nature, 2020.
https://doi.org/10.1007/s00222-020-00964-9.
ieee: R. Killip, J. Murphy, and M. Vişan, “Invariance of white noise for KdV on
the line,” Inventiones mathematicae, vol. 222, no. 1. Springer Nature,
pp. 203–282, 2020.
ista: Killip R, Murphy J, Vişan M. 2020. Invariance of white noise for KdV on the
line. Inventiones mathematicae. 222(1), 203–282.
mla: Killip, Rowan, et al. “Invariance of White Noise for KdV on the Line.” Inventiones
Mathematicae, vol. 222, no. 1, Springer Nature, 2020, pp. 203–82, doi:10.1007/s00222-020-00964-9.
short: R. Killip, J. Murphy, M. Vişan, Inventiones Mathematicae 222 (2020) 203–282.
das_tickbox: '1'
date_created: 2026-06-19T07:56:16Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2026-06-25T08:39:30Z
day: '01'
doi: 10.1007/s00222-020-00964-9
extern: '1'
external_id:
arxiv:
- '1904.11910'
intvolume: ' 222'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1904.11910
month: '10'
oa: 1
oa_version: Preprint
page: 203-282
publication: Inventiones mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Invariance of white noise for KdV on the line
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 222
year: '2020'
...
---
OA_place: repository
OA_type: green
_id: '1457'
abstract:
- lang: eng
text: 'Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov
and Stromdnger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation
but is not clearly related to the physical motivation; the second is the opposite.
Furthermore, it is far from obvious that mirror partners in one sense will also
be mirror partners in the other. This paper concerns a class of examples that
can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also
equal. This provides significant evidence in support of SYZ. Moreover, the examples
are of great interest in their own right: they are spaces of flat SLr-connections
on a smooth curve. The mirror is the corresponding space for the Langlands dual
group PGLr. These examples therefore throw a bridge from mirror symmetry to the
duality theory of Lie groups and, more broadly, to the geometric Langlands program.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tamas
full_name: Hausel, Tamas
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
orcid: 0000-0002-9582-2634
- first_name: Michael
full_name: Thaddeus, Michael
last_name: Thaddeus
citation:
ama: Hausel T, Thaddeus M. Mirror symmetry, langlands duality, and the Hitchin system.
Inventiones Mathematicae. 2003;153:197-229. doi:10.1007/s00222-003-0286-7
apa: Hausel, T., & Thaddeus, M. (2003). Mirror symmetry, langlands duality,
and the Hitchin system. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-003-0286-7
chicago: Hausel, Tamás, and Michael Thaddeus. “Mirror Symmetry, Langlands Duality,
and the Hitchin System.” Inventiones Mathematicae. Springer Nature, 2003.
https://doi.org/10.1007/s00222-003-0286-7.
ieee: T. Hausel and M. Thaddeus, “Mirror symmetry, langlands duality, and the Hitchin
system,” Inventiones Mathematicae, vol. 153. Springer Nature, pp. 197–229,
2003.
ista: Hausel T, Thaddeus M. 2003. Mirror symmetry, langlands duality, and the Hitchin
system. Inventiones Mathematicae. 153, 197–229.
mla: Hausel, Tamás, and Michael Thaddeus. “Mirror Symmetry, Langlands Duality, and
the Hitchin System.” Inventiones Mathematicae, vol. 153, Springer Nature,
2003, pp. 197–229, doi:10.1007/s00222-003-0286-7.
short: T. Hausel, M. Thaddeus, Inventiones Mathematicae 153 (2003) 197–229.
date_created: 2018-12-11T11:52:08Z
date_published: 2003-07-01T00:00:00Z
date_updated: 2026-05-28T11:54:13Z
day: '01'
doi: 10.1007/s00222-003-0286-7
extern: '1'
external_id:
arxiv:
- '0205236'
intvolume: ' 153'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.math/0205236'
month: '07'
oa: 1
oa_version: Preprint
page: 197 - 229
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
publist_id: '5738'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mirror symmetry, langlands duality, and the Hitchin system
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 153
year: '2003'
...