--- _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thanks go to Christof Geiss, Bernard Leclerc and Jan Schröer for explaining their work but also for sharing some unpublished results with us.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' ...