[{"oa_version":"None","title":"Locally free representations of quivers over commutative Frobenius algebras","status":"public","intvolume":" 30","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_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."}],"issue":"2","type":"journal_article","date_published":"2024-01-27T00:00:00Z","article_type":"original","publication":"Selecta Mathematica","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","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.","short":"T. Hausel, E. Letellier, F. Rodriguez-Villegas, Selecta Mathematica 30 (2024).","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.","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."},"day":"27","article_processing_charge":"No","scopus_import":"1","date_created":"2024-02-04T23:00:53Z","date_updated":"2024-02-05T12:58:21Z","volume":30,"author":[{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás","last_name":"Hausel","full_name":"Hausel, Tamás"},{"first_name":"Emmanuel","last_name":"Letellier","full_name":"Letellier, Emmanuel"},{"full_name":"Rodriguez-Villegas, Fernando","first_name":"Fernando","last_name":"Rodriguez-Villegas"}],"publication_status":"epub_ahead","publisher":"Springer Nature","department":[{"_id":"TaHa"}],"year":"2024","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","language":[{"iso":"eng"}],"doi":"10.1007/s00029-023-00914-2","quality_controlled":"1","month":"01","publication_identifier":{"issn":["1022-1824"],"eissn":["1420-9020"]}},{"keyword":["General Mathematics"],"day":"05","article_processing_charge":"Yes (via OA deal)","publication":"International Mathematics Research Notices","citation":{"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).","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.","ama":"Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024. doi:10.1093/imrn/rnae005","ista":"Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices.","ieee":"S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” International Mathematics Research Notices. Oxford University Press, 2024.","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"},"article_type":"original","date_published":"2024-02-05T00:00:00Z","type":"journal_article","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 ."}],"_id":"14986","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Tamely ramified geometric Langlands correspondence in positive characteristic","status":"public","oa_version":"Published Version","month":"02","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"external_id":{"arxiv":["1810.12491"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1093/imrn/rnae005"}],"quality_controlled":"1","project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"doi":"10.1093/imrn/rnae005","language":[{"iso":"eng"}],"ec_funded":1,"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.","year":"2024","publication_status":"epub_ahead","publisher":"Oxford University Press","department":[{"_id":"TaHa"}],"author":[{"last_name":"Shen","first_name":"Shiyu","id":"544cccd3-9005-11ec-87bc-94aef1c5b814","full_name":"Shen, Shiyu"}],"date_created":"2024-02-14T12:16:17Z","date_updated":"2024-02-19T10:22:44Z"},{"publication_identifier":{"eissn":["2045-2322"]},"month":"01","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["001003345000051"]},"oa":1,"isi":1,"quality_controlled":"1","doi":"10.1038/s41598-022-19827-9","language":[{"iso":"eng"}],"article_number":"468","file_date_updated":"2023-01-23T07:53:23Z","license":"https://creativecommons.org/licenses/by/4.0/","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.","year":"2023","publisher":"Springer Nature","department":[{"_id":"TaHa"}],"publication_status":"published","author":[{"first_name":"Arturo","last_name":"Gómez","full_name":"Gómez, Arturo"},{"full_name":"Oliveira, Goncalo","id":"58abbde8-f455-11eb-a497-98c8fd71b905","first_name":"Goncalo","last_name":"Oliveira"}],"volume":13,"date_created":"2023-01-22T23:00:55Z","date_updated":"2023-08-01T12:31:40Z","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"10","citation":{"ama":"Gómez A, Oliveira G. New approaches to epidemic modeling on networks. Scientific Reports. 2023;13. doi:10.1038/s41598-022-19827-9","ista":"Gómez A, Oliveira G. 2023. New approaches to epidemic modeling on networks. Scientific Reports. 13, 468.","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","ieee":"A. Gómez and G. Oliveira, “New approaches to epidemic modeling on networks,” Scientific Reports, vol. 13. Springer Nature, 2023.","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).","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."},"publication":"Scientific Reports","article_type":"original","date_published":"2023-01-10T00:00:00Z","type":"journal_article","abstract":[{"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.","lang":"eng"}],"_id":"12329","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 13","status":"public","title":"New approaches to epidemic modeling on networks","ddc":["510"],"file":[{"access_level":"open_access","file_name":"2023_ScientificReports_Gomez.pdf","content_type":"application/pdf","file_size":2167792,"creator":"dernst","relation":"main_file","file_id":"12336","checksum":"a8b83739f4a951e83e0b2a778f03b327","success":1,"date_created":"2023-01-23T07:53:23Z","date_updated":"2023-01-23T07:53:23Z"}],"oa_version":"Published Version"},{"day":"15","article_processing_charge":"No","scopus_import":"1","date_published":"2023-07-15T00:00:00Z","article_type":"original","publication":"Physical Review B","citation":{"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.","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","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.","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","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.","short":"G. Bighin, Q.P. Ho, M. Lemeshko, T.V. Tscherbul, Physical Review B 108 (2023).","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."},"abstract":[{"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.","lang":"eng"}],"issue":"4","type":"journal_article","oa_version":"Preprint","title":"Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling","status":"public","intvolume":" 108","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13966","month":"07","publication_identifier":{"issn":["2469-9950"],"eissn":["2469-9969"]},"language":[{"iso":"eng"}],"doi":"10.1103/PhysRevB.108.045115","quality_controlled":"1","project":[{"call_identifier":"FWF","name":"A path-integral approach to composite impurities","grant_number":"M02641","_id":"26986C82-B435-11E9-9278-68D0E5697425"},{"grant_number":"M02751","_id":"26B96266-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Algebro-Geometric Applications of Factorization Homology"},{"_id":"26031614-B435-11E9-9278-68D0E5697425","grant_number":"P29902","call_identifier":"FWF","name":"Quantum rotations in the presence of a many-body environment"},{"call_identifier":"H2020","name":"Angulon: physics and applications of a new quasiparticle","grant_number":"801770","_id":"2688CF98-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":["2203.12666"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2203.12666"}],"ec_funded":1,"article_number":"045115","date_updated":"2023-08-07T08:41:29Z","date_created":"2023-08-06T22:01:10Z","volume":108,"author":[{"full_name":"Bighin, Giacomo","last_name":"Bighin","first_name":"Giacomo","orcid":"0000-0001-8823-9777","id":"4CA96FD4-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Ho","first_name":"Quoc P","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","full_name":"Ho, Quoc P"},{"full_name":"Lemeshko, Mikhail","last_name":"Lemeshko","first_name":"Mikhail","orcid":"0000-0002-6990-7802","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Tscherbul, T. V.","last_name":"Tscherbul","first_name":"T. V."}],"publication_status":"published","publisher":"American Physical Society","department":[{"_id":"MiLe"},{"_id":"TaHa"}],"year":"2023","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."},{"publication_status":"published","department":[{"_id":"TaHa"}],"publisher":"Cambridge University Press","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","year":"2023","date_created":"2023-08-27T22:01:16Z","date_updated":"2023-12-13T12:18:18Z","volume":11,"author":[{"full_name":"Mauri, Mirko","last_name":"Mauri","first_name":"Mirko","id":"2cf70c34-09c1-11ed-bd8d-c34fac206130"},{"first_name":"Evgeny","last_name":"Shinder","full_name":"Shinder, Evgeny"}],"article_number":"e66","file_date_updated":"2023-09-05T06:43:11Z","ec_funded":1,"quality_controlled":"1","isi":1,"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"external_id":{"isi":["001041926700001"],"arxiv":["2212.06786"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1017/fms.2023.65","month":"08","publication_identifier":{"eissn":["2050-5094"]},"status":"public","ddc":["510"],"title":"Homological Bondal-Orlov localization conjecture for rational singularities","intvolume":" 11","_id":"14239","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2023_ForumMathematics_Mauri.pdf","file_size":280865,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"14266","checksum":"c36241750cc5cb06890aec0ecdfee626","success":1,"date_created":"2023-09-05T06:43:11Z","date_updated":"2023-09-05T06:43:11Z"}],"type":"journal_article","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 ."}],"article_type":"original","publication":"Forum of Mathematics, Sigma","citation":{"short":"M. Mauri, E. Shinder, Forum of Mathematics, Sigma 11 (2023).","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.","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.","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","ieee":"M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture for rational singularities,” Forum of Mathematics, Sigma, vol. 11. Cambridge University Press, 2023.","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","ista":"Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 11, e66."},"date_published":"2023-08-03T00:00:00Z","scopus_import":"1","day":"03","has_accepted_license":"1","article_processing_charge":"Yes"},{"volume":30,"date_updated":"2024-01-16T12:00:47Z","date_created":"2023-07-23T22:01:14Z","author":[{"full_name":"Huybrechts, D.","last_name":"Huybrechts","first_name":"D."},{"last_name":"Mauri","first_name":"Mirko","id":"2cf70c34-09c1-11ed-bd8d-c34fac206130","full_name":"Mauri, Mirko"}],"department":[{"_id":"TaHa"}],"publisher":"International Press","publication_status":"published","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.","year":"2023","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.4310/mrl.2023.v30.n1.a6","project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"quality_controlled":"1","isi":1,"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.01587","open_access":"1"}],"external_id":{"isi":["001027656000006"],"arxiv":["2108.01587"]},"publication_identifier":{"issn":["1073-2780"],"eissn":["1945-001X"]},"month":"06","oa_version":"Preprint","intvolume":" 30","title":"On type II degenerations of hyperkähler manifolds","status":"public","_id":"13268","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","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."}],"type":"journal_article","date_published":"2023-06-21T00:00:00Z","page":"125-141","article_type":"original","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","ista":"Huybrechts D, Mauri M. 2023. On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. 30(1), 125–141.","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.","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","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.","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."},"publication":"Mathematical Research Letters","article_processing_charge":"No","day":"21","scopus_import":"1"},{"oa_version":"Published Version","file":[{"file_id":"14910","relation":"main_file","date_updated":"2024-01-30T12:56:00Z","date_created":"2024-01-30T12:56:00Z","success":1,"checksum":"2af4d2d6a8ae42f7d3fba0188e79ae82","file_name":"2023_ProcLondonMathSoc_Hausel.pdf","access_level":"open_access","creator":"dernst","file_size":651335,"content_type":"application/pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14244","intvolume":" 127","title":"Arithmetic and metric aspects of open de Rham spaces","ddc":["510"],"status":"public","issue":"4","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."}],"type":"journal_article","date_published":"2023-10-01T00:00:00Z","citation":{"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.","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.","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.","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","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.","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"},"publication":"Proceedings of the London Mathematical Society","page":"958-1027","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","author":[{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás","last_name":"Hausel","full_name":"Hausel, Tamás"},{"first_name":"Michael Lennox","last_name":"Wong","full_name":"Wong, Michael Lennox"},{"full_name":"Wyss, Dimitri","last_name":"Wyss","first_name":"Dimitri"}],"volume":127,"date_updated":"2024-01-30T12:56:10Z","date_created":"2023-08-27T22:01:18Z","year":"2023","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).","publisher":"Wiley","department":[{"_id":"TaHa"}],"publication_status":"published","ec_funded":1,"file_date_updated":"2024-01-30T12:56:00Z","doi":"10.1112/plms.12555","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1807.04057"],"isi":["001049312700001"]},"project":[{"call_identifier":"FP7","name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425","grant_number":"320593"},{"_id":"25E6C798-B435-11E9-9278-68D0E5697425","grant_number":"153627","name":"Arithmetic quantization of character and quiver varities"}],"quality_controlled":"1","isi":1,"publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"month":"10"},{"title":"Loop Grassmannians of Quivers and Affine Quantum Groups","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12303","oa_version":"Preprint","alternative_title":["Trends in Mathematics"],"type":"book_chapter","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)."}],"page":"347-392","citation":{"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.","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.","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","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","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.","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."},"publication":"Representation Theory and Algebraic Geometry","date_published":"2022-06-16T00:00:00Z","series_title":"TM","scopus_import":"1","article_processing_charge":"No","day":"16","publisher":"Springer Nature; Birkhäuser","editor":[{"full_name":"Baranovskky, Vladimir","last_name":"Baranovskky","first_name":"Vladimir"},{"first_name":"Nicolas","last_name":"Guay","full_name":"Guay, Nicolas"},{"last_name":"Schedler","first_name":"Travis","full_name":"Schedler, Travis"}],"department":[{"_id":"TaHa"}],"publication_status":"published","year":"2022","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.","date_updated":"2023-01-27T07:07:31Z","date_created":"2023-01-16T10:06:41Z","edition":"1","author":[{"full_name":"Mirković, Ivan","first_name":"Ivan","last_name":"Mirković"},{"last_name":"Yang","first_name":"Yaping","full_name":"Yang, Yaping"},{"last_name":"Zhao","first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","full_name":"Zhao, Gufang"}],"place":"Cham","ec_funded":1,"project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","grant_number":"320593","call_identifier":"FP7","name":"Arithmetic and physics of Higgs moduli spaces"}],"quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1810.10095","open_access":"1"}],"external_id":{"arxiv":["1810.10095"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-82007-7_8","publication_identifier":{"issn":["2297-0215"],"eisbn":["9783030820077"],"eissn":["2297-024X"],"isbn":["9783030820060"]},"month":"06"},{"publication_status":"published","department":[{"_id":"TaHa"}],"publisher":"Wiley","year":"2022","acknowledgement":"We warmly thank S. Gukov for valuable discussions on the GPPV invariant ̂Z𝑎(𝑀3; 𝑞). 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.","date_updated":"2023-08-02T06:53:51Z","date_created":"2021-08-31T12:51:40Z","volume":105,"author":[{"id":"41B03CD0-62AE-11E9-84EF-0718E6697425","last_name":"Mistegaard","first_name":"William","full_name":"Mistegaard, William"},{"full_name":"Andersen, Jørgen Ellegaard","last_name":"Andersen","first_name":"Jørgen Ellegaard"}],"file_date_updated":"2022-03-24T11:42:25Z","ec_funded":1,"quality_controlled":"1","isi":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"external_id":{"arxiv":["1811.05376"],"isi":["000755205700001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1112/jlms.12506","month":"03","publication_identifier":{"eissn":["1469-7750"]},"ddc":["510"],"title":"Resurgence analysis of quantum invariants of Seifert fibered homology spheres","status":"public","intvolume":" 105","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9977","file":[{"file_size":649130,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2022_JourLondonMathSoc_Andersen.pdf","checksum":"9c72327d39f34f1a6eaa98fa4b8493f2","success":1,"date_created":"2022-03-24T11:42:25Z","date_updated":"2022-03-24T11:42:25Z","relation":"main_file","file_id":"10917"}],"oa_version":"Published Version","type":"journal_article","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."}],"issue":"2","article_type":"original","page":"709-764","publication":"Journal of the London Mathematical Society","citation":{"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.","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","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.","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","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.","short":"W. Mistegaard, J.E. Andersen, Journal of the London Mathematical Society 105 (2022) 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."},"date_published":"2022-03-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1"},{"date_published":"2022-05-01T00:00:00Z","citation":{"ista":"Hausel T, Hitchin N. 2022. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. 228, 893–989.","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.","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","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","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.","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."},"publication":"Inventiones Mathematicae","page":"893-989","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","file":[{"creator":"dernst","content_type":"application/pdf","file_size":1069538,"file_name":"2022_InventionesMahtematicae_Hausel.pdf","access_level":"open_access","date_created":"2023-02-27T07:30:47Z","date_updated":"2023-02-27T07:30:47Z","success":1,"checksum":"a382ba75acebc9adfb8fe56247cb410e","file_id":"12687","relation":"main_file"}],"oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10704","intvolume":" 228","status":"public","ddc":["510"],"title":"Very stable Higgs bundles, equivariant multiplicity and mirror symmetry","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."}],"type":"journal_article","doi":"10.1007/s00222-021-01093-7","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["2101.08583"],"isi":["000745495400001"]},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"isi":1,"quality_controlled":"1","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"month":"05","related_material":{"link":[{"relation":"press_release","description":"News on the ISTA Website","url":"https://ista.ac.at/en/news/the-tip-of-the-mathematical-iceberg/"}]},"author":[{"full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel","first_name":"Tamás"},{"first_name":"Nigel","last_name":"Hitchin","full_name":"Hitchin, Nigel"}],"volume":228,"date_created":"2022-01-30T23:01:34Z","date_updated":"2023-08-02T14:03:20Z","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).","year":"2022","publisher":"Springer Nature","department":[{"_id":"TaHa"}],"publication_status":"published","file_date_updated":"2023-02-27T07:30:47Z"}]