--- _id: '14930' abstract: - lang: eng text: In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable locally free representations of fixed rank is independent of the orientation of Q. We also prove that the number of isomorphism classes of locally free absolutely indecomposable representations of the preprojective algebra of Q over R equals the number of isomorphism classes of locally free absolutely indecomposable representations of Q over R[t]/(t2). Using these results together with results of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification of pairs (Q, R) such that the set of isomorphism classes of indecomposable locally free representations of Q over R is finite. Finally when the representation is free of rank 1 at each vertex of Q, we study the function that counts the number of isomorphism classes of absolutely indecomposable locally free representations of Q over the Frobenius algebra Fq[t]/(tr). We prove that they are polynomial in q and their generating function is rational and satisfies a functional equation. acknowledgement: Special thanks go to Christof Geiss, Bernard Leclerc and Jan Schröer for explaining their work but also for sharing some unpublished results with us. We also thank the referee for many useful suggestions. We would like to thank Tommaso Scognamiglio for pointing out a mistake in the proof of Proposition 5.17 in an earlier version of the paper. We would like also to thank Alexander Beilinson, Bill Crawley-Boevey, Joel Kamnitzer, and Peng Shan for useful discussions. article_number: '20' article_processing_charge: No article_type: original author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Emmanuel full_name: Letellier, Emmanuel last_name: Letellier - first_name: Fernando full_name: Rodriguez-Villegas, Fernando last_name: Rodriguez-Villegas citation: ama: Hausel T, Letellier E, Rodriguez-Villegas F. Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. 2024;30(2). doi:10.1007/s00029-023-00914-2 apa: Hausel, T., Letellier, E., & Rodriguez-Villegas, F. (2024). Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. Springer Nature. https://doi.org/10.1007/s00029-023-00914-2 chicago: Hausel, Tamás, Emmanuel Letellier, and Fernando Rodriguez-Villegas. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” Selecta Mathematica. Springer Nature, 2024. https://doi.org/10.1007/s00029-023-00914-2. ieee: T. Hausel, E. Letellier, and F. Rodriguez-Villegas, “Locally free representations of quivers over commutative Frobenius algebras,” Selecta Mathematica, vol. 30, no. 2. Springer Nature, 2024. ista: Hausel T, Letellier E, Rodriguez-Villegas F. 2024. Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. 30(2), 20. mla: Hausel, Tamás, et al. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” Selecta Mathematica, vol. 30, no. 2, 20, Springer Nature, 2024, doi:10.1007/s00029-023-00914-2. short: T. Hausel, E. Letellier, F. Rodriguez-Villegas, Selecta Mathematica 30 (2024). date_created: 2024-02-04T23:00:53Z date_published: 2024-01-27T00:00:00Z date_updated: 2024-02-05T12:58:21Z day: '27' department: - _id: TaHa doi: 10.1007/s00029-023-00914-2 intvolume: ' 30' issue: '2' language: - iso: eng month: '01' oa_version: None publication: Selecta Mathematica publication_identifier: eissn: - 1420-9020 issn: - 1022-1824 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Locally free representations of quivers over commutative Frobenius algebras type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2024' ... --- _id: '14986' abstract: - lang: eng text: We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k). Let k be an algebraically closed field of characteristic p>n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod) of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman to the tamely ramified case. We also prove a correspondence between flat connections on X with regular singularities and meromorphic Higgs bundles on the Frobenius twist X(1) of X with first order poles . acknowledgement: "This work was supported by the NSF [DMS-1502125to S.S.]; and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement [101034413 to S.S.].\r\nI would like to thank my advisor Tom Nevins for many helpful discussions on this subject and for his comments on this paper. I would like to thank Christopher Dodd, Michael Groechenig, and Tamas Hausel for helpful conversations. I would like to thank Tsao-Hsien Chen for useful comments on an earlier version of this paper." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Shiyu full_name: Shen, Shiyu id: 544cccd3-9005-11ec-87bc-94aef1c5b814 last_name: Shen citation: ama: Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024. doi:10.1093/imrn/rnae005 apa: Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae005 chicago: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae005. ieee: S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” International Mathematics Research Notices. Oxford University Press, 2024. ista: Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. mla: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices, Oxford University Press, 2024, doi:10.1093/imrn/rnae005. short: S. Shen, International Mathematics Research Notices (2024). date_created: 2024-02-14T12:16:17Z date_published: 2024-02-05T00:00:00Z date_updated: 2024-02-19T10:22:44Z day: '05' department: - _id: TaHa doi: 10.1093/imrn/rnae005 ec_funded: 1 external_id: arxiv: - '1810.12491' keyword: - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1093/imrn/rnae005 month: '02' 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: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: epub_ahead publisher: Oxford University Press quality_controlled: '1' status: public title: Tamely ramified geometric Langlands correspondence in positive characteristic type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- _id: '12329' abstract: - lang: eng text: In this article, we develop two independent and new approaches to model epidemic spread in a network. Contrary to the most studied models, those developed here allow for contacts with different probabilities of transmitting the disease (transmissibilities). We then examine each of these models using some mean field type approximations. The first model looks at the late-stage effects of an epidemic outbreak and allows for the computation of the probability that a given vertex was infected. This computation is based on a mean field approximation and only depends on the number of contacts and their transmissibilities. This approach shares many similarities with percolation models in networks. The second model we develop is a dynamic model which we analyze using a mean field approximation which highly reduces the dimensionality of the system. In particular, the original system which individually analyses each vertex of the network is reduced to one with as many equations as different transmissibilities. Perhaps the greatest contribution of this article is the observation that, in both these models, the existence and size of an epidemic outbreak are linked to the properties of a matrix which we call the R-matrix. This is a generalization of the basic reproduction number which more precisely characterizes the main routes of infection. acknowledgement: Gonçalo Oliveira is supported by the NOMIS Foundation, Fundação Serrapilheira 1812-27395, by CNPq grants 428959/2018-0 and 307475/2018-2, and by FAPERJ through the grant Jovem Cientista do Nosso Estado E-26/202.793/2019. article_number: '468' article_processing_charge: No article_type: original author: - first_name: Arturo full_name: Gómez, Arturo last_name: Gómez - first_name: Goncalo full_name: Oliveira, Goncalo id: 58abbde8-f455-11eb-a497-98c8fd71b905 last_name: Oliveira citation: ama: Gómez A, Oliveira G. New approaches to epidemic modeling on networks. Scientific Reports. 2023;13. doi:10.1038/s41598-022-19827-9 apa: Gómez, A., & Oliveira, G. (2023). New approaches to epidemic modeling on networks. Scientific Reports. Springer Nature. https://doi.org/10.1038/s41598-022-19827-9 chicago: Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on Networks.” Scientific Reports. Springer Nature, 2023. https://doi.org/10.1038/s41598-022-19827-9. ieee: A. Gómez and G. Oliveira, “New approaches to epidemic modeling on networks,” Scientific Reports, vol. 13. Springer Nature, 2023. ista: Gómez A, Oliveira G. 2023. New approaches to epidemic modeling on networks. Scientific Reports. 13, 468. mla: Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on Networks.” Scientific Reports, vol. 13, 468, Springer Nature, 2023, doi:10.1038/s41598-022-19827-9. short: A. Gómez, G. Oliveira, Scientific Reports 13 (2023). date_created: 2023-01-22T23:00:55Z date_published: 2023-01-10T00:00:00Z date_updated: 2023-08-01T12:31:40Z day: '10' ddc: - '510' department: - _id: TaHa doi: 10.1038/s41598-022-19827-9 external_id: isi: - '001003345000051' file: - access_level: open_access checksum: a8b83739f4a951e83e0b2a778f03b327 content_type: application/pdf creator: dernst date_created: 2023-01-23T07:53:23Z date_updated: 2023-01-23T07:53:23Z file_id: '12336' file_name: 2023_ScientificReports_Gomez.pdf file_size: 2167792 relation: main_file success: 1 file_date_updated: 2023-01-23T07:53:23Z has_accepted_license: '1' intvolume: ' 13' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version publication: Scientific Reports publication_identifier: eissn: - 2045-2322 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: New approaches to epidemic modeling on networks 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: 13 year: '2023' ... --- _id: '13966' abstract: - lang: eng text: We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the Møller-Plesset (MPn) perturbation series, obtaining accurate correlation energies up to n=5, with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecular many-fermion correlation problem, opening up the possibility of low-scaling, accurate stochastic computations for a wide class of many-body systems described by Hugenholtz diagrams. acknowledgement: We acknowledge stimulating discussions with Sergey Varganov, Artur Izmaylov, Jacek Kłos, Piotr Żuchowski, Dominika Zgid, Nikolay Prokof'ev, Boris Svistunov, Robert Parrish, and Andreas Heßelmann. G.B. and Q.P.H. acknowledge support from the Austrian Science Fund (FWF) under Projects No. M2641-N27 and No. M2751. M.L. acknowledges support by the FWF under Project No. P29902-N27, and by the European Research Council (ERC) Starting Grant No. 801770 (ANGULON). T.V.T. was supported by the NSF CAREER award No. PHY-2045681. This work is supported by the German Research Foundation (DFG) under Germany's Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster). The authors acknowledge support by the state of Baden-Württemberg through bwHPC. article_number: '045115' article_processing_charge: No article_type: original author: - first_name: Giacomo full_name: Bighin, Giacomo id: 4CA96FD4-F248-11E8-B48F-1D18A9856A87 last_name: Bighin orcid: 0000-0001-8823-9777 - first_name: Quoc P full_name: Ho, Quoc P id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87 last_name: Ho - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 - first_name: T. V. full_name: Tscherbul, T. V. last_name: Tscherbul citation: ama: 'Bighin G, Ho QP, Lemeshko M, Tscherbul TV. Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling. Physical Review B. 2023;108(4). doi:10.1103/PhysRevB.108.045115' apa: 'Bighin, G., Ho, Q. P., Lemeshko, M., & Tscherbul, T. V. (2023). Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling. Physical Review B. American Physical Society. https://doi.org/10.1103/PhysRevB.108.045115' chicago: 'Bighin, Giacomo, Quoc P Ho, Mikhail Lemeshko, and T. V. Tscherbul. “Diagrammatic Monte Carlo for Electronic Correlation in Molecules: High-Order Many-Body Perturbation Theory with Low Scaling.” Physical Review B. American Physical Society, 2023. https://doi.org/10.1103/PhysRevB.108.045115.' ieee: 'G. Bighin, Q. P. Ho, M. Lemeshko, and T. V. Tscherbul, “Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling,” Physical Review B, vol. 108, no. 4. American Physical Society, 2023.' ista: 'Bighin G, Ho QP, Lemeshko M, Tscherbul TV. 2023. Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling. Physical Review B. 108(4), 045115.' mla: 'Bighin, Giacomo, et al. “Diagrammatic Monte Carlo for Electronic Correlation in Molecules: High-Order Many-Body Perturbation Theory with Low Scaling.” Physical Review B, vol. 108, no. 4, 045115, American Physical Society, 2023, doi:10.1103/PhysRevB.108.045115.' short: G. Bighin, Q.P. Ho, M. Lemeshko, T.V. Tscherbul, Physical Review B 108 (2023). date_created: 2023-08-06T22:01:10Z date_published: 2023-07-15T00:00:00Z date_updated: 2023-08-07T08:41:29Z day: '15' department: - _id: MiLe - _id: TaHa doi: 10.1103/PhysRevB.108.045115 ec_funded: 1 external_id: arxiv: - '2203.12666' intvolume: ' 108' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2203.12666 month: '07' oa: 1 oa_version: Preprint project: - _id: 26986C82-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02641 name: A path-integral approach to composite impurities - _id: 26B96266-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02751 name: Algebro-Geometric Applications of Factorization Homology - _id: 26031614-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P29902 name: Quantum rotations in the presence of a many-body environment - _id: 2688CF98-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '801770' name: 'Angulon: physics and applications of a new quasiparticle' publication: Physical Review B publication_identifier: eissn: - 2469-9969 issn: - 2469-9950 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: 'Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 108 year: '2023' ... --- _id: '14239' abstract: - lang: eng text: "Given a resolution of rational singularities π:X~→X over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor \ Rπ∗:Db(X~)→Db(X)\r\n between bounded derived categories of coherent sheaves generates Db(X)\r\n as a triangulated category. This gives a weak version of the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21]. The same result is established more generally for proper (not necessarily birational) morphisms π:X~→X , with X~\r\n smooth, satisfying Rπ∗(OX~)=OX ." acknowledgement: "We thank Agnieszka Bodzenta-Skibińska, Paolo Cascini, Wahei Hara, Sándor Kovács, Alexander Kuznetsov, Mircea Musta ă, Nebojsa Pavic, Pavel Sechin, and Michael Wemyss for discussions and e-mail correspondence. We also thank the anonymous referee for the helpful comments. M.M. was supported by the Institute of Science and Technology Austria. 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. E.S. was partially supported by the EPSRC grant EP/T019379/1 “Derived categories and algebraic K-theory of singularities”, and by the ERC Synergy grant “Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties.”\r\n\r\n" article_number: e66 article_processing_charge: Yes article_type: original author: - first_name: Mirko full_name: Mauri, Mirko id: 2cf70c34-09c1-11ed-bd8d-c34fac206130 last_name: Mauri - first_name: Evgeny full_name: Shinder, Evgeny last_name: Shinder citation: ama: Mauri M, Shinder E. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 2023;11. doi:10.1017/fms.2023.65 apa: Mauri, M., & Shinder, E. (2023). Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.65 chicago: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” Forum of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.65. ieee: M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture for rational singularities,” Forum of Mathematics, Sigma, vol. 11. Cambridge University Press, 2023. ista: Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 11, e66. mla: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” Forum of Mathematics, Sigma, vol. 11, e66, Cambridge University Press, 2023, doi:10.1017/fms.2023.65. short: M. Mauri, E. Shinder, Forum of Mathematics, Sigma 11 (2023). date_created: 2023-08-27T22:01:16Z date_published: 2023-08-03T00:00:00Z date_updated: 2023-12-13T12:18:18Z day: '03' ddc: - '510' department: - _id: TaHa doi: 10.1017/fms.2023.65 ec_funded: 1 external_id: arxiv: - '2212.06786' isi: - '001041926700001' file: - access_level: open_access checksum: c36241750cc5cb06890aec0ecdfee626 content_type: application/pdf creator: dernst date_created: 2023-09-05T06:43:11Z date_updated: 2023-09-05T06:43:11Z file_id: '14266' file_name: 2023_ForumMathematics_Mauri.pdf file_size: 280865 relation: main_file success: 1 file_date_updated: 2023-09-05T06:43:11Z has_accepted_license: '1' intvolume: ' 11' isi: 1 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: Forum of Mathematics, Sigma publication_identifier: eissn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Homological Bondal-Orlov localization conjecture for rational singularities tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2023' ... --- _id: '13268' abstract: - lang: eng text: We give a simple argument to prove Nagai’s conjecture for type II degenerations of compact hyperkähler manifolds and cohomology classes of middle degree. Under an additional assumption, the techniques yield the conjecture in arbitrary degree. This would complete the proof of Nagai’s conjecture in general, as it was proved already for type I degenerations by Kollár, Laza, Saccà, and Voisin [10] and independently by Soldatenkov [18], while it is immediate for type III degenerations. Our arguments are close in spirit to a recent paper by Harder [8] proving similar results for the restrictive class of good degenerations. acknowledgement: The first author is supported by the ERC Synergy Grant HyperK. The second author is supported by the Max Planck Institute for Mathematics and the Institute of Science and Technology Austria. 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. article_processing_charge: No article_type: original author: - first_name: D. full_name: Huybrechts, D. last_name: Huybrechts - first_name: Mirko full_name: Mauri, Mirko id: 2cf70c34-09c1-11ed-bd8d-c34fac206130 last_name: Mauri citation: ama: Huybrechts D, Mauri M. On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. 2023;30(1):125-141. doi:10.4310/mrl.2023.v30.n1.a6 apa: Huybrechts, D., & Mauri, M. (2023). On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. International Press. https://doi.org/10.4310/mrl.2023.v30.n1.a6 chicago: Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.” Mathematical Research Letters. International Press, 2023. https://doi.org/10.4310/mrl.2023.v30.n1.a6. ieee: D. Huybrechts and M. Mauri, “On type II degenerations of hyperkähler manifolds,” Mathematical Research Letters, vol. 30, no. 1. International Press, pp. 125–141, 2023. ista: Huybrechts D, Mauri M. 2023. On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. 30(1), 125–141. mla: Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.” Mathematical Research Letters, vol. 30, no. 1, International Press, 2023, pp. 125–41, doi:10.4310/mrl.2023.v30.n1.a6. short: D. Huybrechts, M. Mauri, Mathematical Research Letters 30 (2023) 125–141. date_created: 2023-07-23T22:01:14Z date_published: 2023-06-21T00:00:00Z date_updated: 2024-01-16T12:00:47Z day: '21' department: - _id: TaHa doi: 10.4310/mrl.2023.v30.n1.a6 ec_funded: 1 external_id: arxiv: - '2108.01587' isi: - '001027656000006' intvolume: ' 30' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2108.01587 month: '06' oa: 1 oa_version: Preprint page: 125-141 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Mathematical Research Letters publication_identifier: eissn: - 1945-001X issn: - 1073-2780 publication_status: published publisher: International Press quality_controlled: '1' scopus_import: '1' status: public title: On type II degenerations of hyperkähler manifolds type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2023' ... --- _id: '14244' abstract: - lang: eng text: "In this paper, we determine the motivic class — in particular, the weight polynomial and conjecturally the Poincaré polynomial — of the open de Rham space, defined and studied by Boalch, of certain moduli spaces of irregular meromorphic connections on the trivial rank \r\n bundle on P1. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild character variety. We also identify the open de Rham spaces with quiver varieties with multiplicities of Yamakawa and Geiss–Leclerc–Schröer. We finish with constructing natural complete hyperkähler metrics on them, which in the four-dimensional cases are expected to be of type ALF." acknowledgement: We would like to thank Gergely Bérczy, Roger Bielawski, Philip Boalch, Sergey Cherkis, Andrew Dancer, Brent Doran, Eloïse Hamilton, Frances Kirwan, Bernard Leclerc, Emmanuel Letellier, Alessia Mandini, Maxence Mayrand, András Némethi, Szilárd Szabó, and Daisuke Yamakawa for discussions related to the paper. We especially thank the referee for an extensive list of very careful comments. At various stages of this project, the authors were supported by the Advanced Grant “Arithmetic and physics of Higgs moduli spaces” no. 320593 of the European Research Council, by grant no. 153627 and NCCR SwissMAP, both funded by the Swiss National Science Foundation as well as by EPF Lausanne and IST Austria. In the final stages of this project, MLW was supported by SFB/TR 45 “Periods, moduli and arithmetic of algebraic varieties,” subproject M08-10 “Moduli of vector bundles on higher-dimensional varieties.” DW was also supported by the Fondation Sciences Mathématiques de Paris, as well as public grants overseen by the Agence national de la recherche (ANR) of France as part of the Investissements d'avenir program, under reference numbers ANR-10-LABX-0098 and ANR-15-CE40-0008 (Défigéo). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Michael Lennox full_name: Wong, Michael Lennox last_name: Wong - first_name: Dimitri full_name: Wyss, Dimitri last_name: Wyss citation: ama: Hausel T, Wong ML, Wyss D. Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. 2023;127(4):958-1027. doi:10.1112/plms.12555 apa: Hausel, T., Wong, M. L., & Wyss, D. (2023). Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.12555 chicago: Hausel, Tamás, Michael Lennox Wong, and Dimitri Wyss. “Arithmetic and Metric Aspects of Open de Rham Spaces.” Proceedings of the London Mathematical Society. Wiley, 2023. https://doi.org/10.1112/plms.12555. ieee: T. Hausel, M. L. Wong, and D. Wyss, “Arithmetic and metric aspects of open de Rham spaces,” Proceedings of the London Mathematical Society, vol. 127, no. 4. Wiley, pp. 958–1027, 2023. ista: Hausel T, Wong ML, Wyss D. 2023. Arithmetic and metric aspects of open de Rham spaces. Proceedings of the London Mathematical Society. 127(4), 958–1027. mla: Hausel, Tamás, et al. “Arithmetic and Metric Aspects of Open de Rham Spaces.” Proceedings of the London Mathematical Society, vol. 127, no. 4, Wiley, 2023, pp. 958–1027, doi:10.1112/plms.12555. short: T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society 127 (2023) 958–1027. date_created: 2023-08-27T22:01:18Z date_published: 2023-10-01T00:00:00Z date_updated: 2024-01-30T12:56:10Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1112/plms.12555 ec_funded: 1 external_id: arxiv: - '1807.04057' isi: - '001049312700001' file: - access_level: open_access checksum: 2af4d2d6a8ae42f7d3fba0188e79ae82 content_type: application/pdf creator: dernst date_created: 2024-01-30T12:56:00Z date_updated: 2024-01-30T12:56:00Z file_id: '14910' file_name: 2023_ProcLondonMathSoc_Hausel.pdf file_size: 651335 relation: main_file success: 1 file_date_updated: 2024-01-30T12:56:00Z has_accepted_license: '1' intvolume: ' 127' isi: 1 issue: '4' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 958-1027 project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces - _id: 25E6C798-B435-11E9-9278-68D0E5697425 grant_number: '153627' name: Arithmetic quantization of character and quiver varities publication: Proceedings of the London Mathematical Society publication_identifier: eissn: - 1460-244X issn: - 0024-6115 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Arithmetic and metric aspects of open de Rham spaces 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: 127 year: '2023' ... --- _id: '12303' abstract: - lang: eng text: We construct for each choice of a quiver Q, a cohomology theory A, and a poset P a “loop Grassmannian” GP(Q,A). This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms. The addition of a “dilation” torus D⊆G2m gives a quantization GPD(Q,A). This construction is motivated by the program of introducing an inner cohomology theory in algebraic geometry adequate for the Geometric Langlands program (Mirković, Some extensions of the notion of loop Grassmannians. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardešić issue. No. 532, 53–74, 2017) and on the construction of affine quantum groups from generalized cohomology theories (Yang and Zhao, Quiver varieties and elliptic quantum groups, preprint. arxiv1708.01418). acknowledgement: I.M. thanks Zhijie Dong for long-term discussions on the material that entered this work. We thank Misha Finkelberg for pointing out errors in earlier versions. His advice and his insistence have led to a much better paper. A part of the writing was done at the conference at IST (Vienna) attended by all coauthors. We therefore thank the organizers of the conference and the support of ERC Advanced Grant Arithmetic and Physics of Higgs moduli spaces No. 320593. The work of I.M. was partially supported by NSF grants. The work of Y.Y. was partially supported by the Australian Research Council (ARC) via the award DE190101231. The work of G.Z. was partially supported by ARC via the award DE190101222. alternative_title: - Trends in Mathematics article_processing_charge: No author: - first_name: Ivan full_name: Mirković, Ivan last_name: Mirković - first_name: Yaping full_name: Yang, Yaping last_name: Yang - first_name: Gufang full_name: Zhao, Gufang id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87 last_name: Zhao citation: ama: 'Mirković I, Yang Y, Zhao G. Loop Grassmannians of Quivers and Affine Quantum Groups. In: Baranovskky V, Guay N, Schedler T, eds. Representation Theory and Algebraic Geometry. 1st ed. TM. Cham: Springer Nature; Birkhäuser; 2022:347-392. doi:10.1007/978-3-030-82007-7_8' apa: 'Mirković, I., Yang, Y., & Zhao, G. (2022). Loop Grassmannians of Quivers and Affine Quantum Groups. In V. Baranovskky, N. Guay, & T. Schedler (Eds.), Representation Theory and Algebraic Geometry (1st ed., pp. 347–392). Cham: Springer Nature; Birkhäuser. https://doi.org/10.1007/978-3-030-82007-7_8' chicago: 'Mirković, Ivan, Yaping Yang, and Gufang Zhao. “Loop Grassmannians of Quivers and Affine Quantum Groups.” In Representation Theory and Algebraic Geometry, edited by Vladimir Baranovskky, Nicolas Guay, and Travis Schedler, 1st ed., 347–92. TM. Cham: Springer Nature; Birkhäuser, 2022. https://doi.org/10.1007/978-3-030-82007-7_8.' ieee: 'I. Mirković, Y. Yang, and G. Zhao, “Loop Grassmannians of Quivers and Affine Quantum Groups,” in Representation Theory and Algebraic Geometry, 1st ed., V. Baranovskky, N. Guay, and T. Schedler, Eds. Cham: Springer Nature; Birkhäuser, 2022, pp. 347–392.' ista: 'Mirković I, Yang Y, Zhao G. 2022.Loop Grassmannians of Quivers and Affine Quantum Groups. In: Representation Theory and Algebraic Geometry. Trends in Mathematics, , 347–392.' mla: Mirković, Ivan, et al. “Loop Grassmannians of Quivers and Affine Quantum Groups.” Representation Theory and Algebraic Geometry, edited by Vladimir Baranovskky et al., 1st ed., Springer Nature; Birkhäuser, 2022, pp. 347–92, doi:10.1007/978-3-030-82007-7_8. short: I. Mirković, Y. Yang, G. Zhao, in:, V. Baranovskky, N. Guay, T. Schedler (Eds.), Representation Theory and Algebraic Geometry, 1st ed., Springer Nature; Birkhäuser, Cham, 2022, pp. 347–392. date_created: 2023-01-16T10:06:41Z date_published: 2022-06-16T00:00:00Z date_updated: 2023-01-27T07:07:31Z day: '16' department: - _id: TaHa doi: 10.1007/978-3-030-82007-7_8 ec_funded: 1 edition: '1' editor: - first_name: Vladimir full_name: Baranovskky, Vladimir last_name: Baranovskky - first_name: Nicolas full_name: Guay, Nicolas last_name: Guay - first_name: Travis full_name: Schedler, Travis last_name: Schedler external_id: arxiv: - '1810.10095' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1810.10095 month: '06' oa: 1 oa_version: Preprint page: 347-392 place: Cham project: - _id: 25E549F4-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '320593' name: Arithmetic and physics of Higgs moduli spaces publication: Representation Theory and Algebraic Geometry publication_identifier: eisbn: - '9783030820077' eissn: - 2297-024X isbn: - '9783030820060' issn: - 2297-0215 publication_status: published publisher: Springer Nature; Birkhäuser quality_controlled: '1' scopus_import: '1' series_title: TM status: public title: Loop Grassmannians of Quivers and Affine Quantum Groups type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2022' ... --- _id: '9977' abstract: - lang: eng text: "For a Seifert fibered homology sphere X we show that the q-series invariant Zˆ0(X; q) introduced by Gukov-Pei-Putrov-Vafa, is a resummation of the Ohtsuki series Z0(X). We show that for every even k ∈ N there exists a full asymptotic expansion of Zˆ0(X; q) for q tending to e 2πi/k, and in particular that the limit Zˆ0(X; e 2πi/k) exists and is equal to the\r\nWRT quantum invariant τk(X). We show that the poles of the Borel transform of Z0(X) coincide with the classical complex Chern-Simons values, which we further show classifies the corresponding components of the moduli space of flat SL(2, C)-connections." acknowledgement: "We warmly thank S. Gukov for valuable discussions on the GPPV invariant ̂Z\U0001D44E(\U0001D4403; \U0001D45E). The first\r\nauthor was supported in part by the center of excellence grant ‘Center for Quantum Geometry\r\nof Moduli Spaces’ from the Danish National Research Foundation (DNRF95) and by the ERCSynergy\r\ngrant ‘ReNewQuantum’. The second author received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 754411." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: William full_name: Mistegaard, William id: 41B03CD0-62AE-11E9-84EF-0718E6697425 last_name: Mistegaard - first_name: Jørgen Ellegaard full_name: Andersen, Jørgen Ellegaard last_name: Andersen citation: ama: Mistegaard W, Andersen JE. Resurgence analysis of quantum invariants of Seifert fibered homology spheres. Journal of the London Mathematical Society. 2022;105(2):709-764. doi:10.1112/jlms.12506 apa: Mistegaard, W., & Andersen, J. E. (2022). Resurgence analysis of quantum invariants of Seifert fibered homology spheres. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12506 chicago: Mistegaard, William, and Jørgen Ellegaard Andersen. “Resurgence Analysis of Quantum Invariants of Seifert Fibered Homology Spheres.” Journal of the London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12506. ieee: W. Mistegaard and J. E. Andersen, “Resurgence analysis of quantum invariants of Seifert fibered homology spheres,” Journal of the London Mathematical Society, vol. 105, no. 2. Wiley, pp. 709–764, 2022. ista: Mistegaard W, Andersen JE. 2022. Resurgence analysis of quantum invariants of Seifert fibered homology spheres. Journal of the London Mathematical Society. 105(2), 709–764. mla: Mistegaard, William, and Jørgen Ellegaard Andersen. “Resurgence Analysis of Quantum Invariants of Seifert Fibered Homology Spheres.” Journal of the London Mathematical Society, vol. 105, no. 2, Wiley, 2022, pp. 709–64, doi:10.1112/jlms.12506. short: W. Mistegaard, J.E. Andersen, Journal of the London Mathematical Society 105 (2022) 709–764. date_created: 2021-08-31T12:51:40Z date_published: 2022-03-01T00:00:00Z date_updated: 2023-08-02T06:53:51Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1112/jlms.12506 ec_funded: 1 external_id: arxiv: - '1811.05376' isi: - '000755205700001' file: - access_level: open_access checksum: 9c72327d39f34f1a6eaa98fa4b8493f2 content_type: application/pdf creator: dernst date_created: 2022-03-24T11:42:25Z date_updated: 2022-03-24T11:42:25Z file_id: '10917' file_name: 2022_JourLondonMathSoc_Andersen.pdf file_size: 649130 relation: main_file success: 1 file_date_updated: 2022-03-24T11:42:25Z has_accepted_license: '1' intvolume: ' 105' isi: 1 issue: '2' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 709-764 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Resurgence analysis of quantum invariants of Seifert fibered homology spheres 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: 105 year: '2022' ... --- _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 author: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - 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. date_created: 2022-01-30T23:01:34Z date_published: 2022-05-01T00:00:00Z date_updated: 2023-08-02T14:03:20Z 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' ...