[{"publication":"Selecta Mathematica","title":"Locally free representations of quivers over commutative Frobenius algebras","issue":"2","scopus_import":"1","citation":{"mla":"Hausel, Tamás, et al. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” <i>Selecta Mathematica</i>, vol. 30, no. 2, 20, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00029-023-00914-2\">10.1007/s00029-023-00914-2</a>.","apa":"Hausel, T., Letellier, E., &#38; Rodriguez-Villegas, F. (2024). Locally free representations of quivers over commutative Frobenius algebras. <i>Selecta Mathematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00029-023-00914-2\">https://doi.org/10.1007/s00029-023-00914-2</a>","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).","ama":"Hausel T, Letellier E, Rodriguez-Villegas F. Locally free representations of quivers over commutative Frobenius algebras. <i>Selecta Mathematica</i>. 2024;30(2). doi:<a href=\"https://doi.org/10.1007/s00029-023-00914-2\">10.1007/s00029-023-00914-2</a>","chicago":"Hausel, Tamás, Emmanuel Letellier, and Fernando Rodriguez-Villegas. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” <i>Selecta Mathematica</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00029-023-00914-2\">https://doi.org/10.1007/s00029-023-00914-2</a>.","ieee":"T. Hausel, E. Letellier, and F. Rodriguez-Villegas, “Locally free representations of quivers over commutative Frobenius algebras,” <i>Selecta Mathematica</i>, vol. 30, no. 2. Springer Nature, 2024."},"publication_status":"epub_ahead","oa_version":"None","day":"27","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."}],"status":"public","date_updated":"2024-02-05T12:58:21Z","volume":30,"article_type":"original","month":"01","quality_controlled":"1","publication_identifier":{"eissn":["1420-9020"],"issn":["1022-1824"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","intvolume":"        30","date_created":"2024-02-04T23:00:53Z","article_number":"20","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.","department":[{"_id":"TaHa"}],"date_published":"2024-01-27T00:00:00Z","author":[{"first_name":"Tamás","full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"},{"last_name":"Letellier","full_name":"Letellier, Emmanuel","first_name":"Emmanuel"},{"last_name":"Rodriguez-Villegas","full_name":"Rodriguez-Villegas, Fernando","first_name":"Fernando"}],"_id":"14930","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00029-023-00914-2","publisher":"Springer Nature","year":"2024"},{"date_published":"2024-02-05T00:00:00Z","author":[{"full_name":"Shen, Shiyu","first_name":"Shiyu","last_name":"Shen","id":"544cccd3-9005-11ec-87bc-94aef1c5b814"}],"oa":1,"_id":"14986","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnae005","publisher":"Oxford University Press","year":"2024","article_type":"original","month":"02","quality_controlled":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","keyword":["General Mathematics"],"date_created":"2024-02-14T12:16:17Z","department":[{"_id":"TaHa"}],"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.","publication_status":"epub_ahead","oa_version":"Published Version","day":"05","ec_funded":1,"abstract":[{"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 .","lang":"eng"}],"status":"public","date_updated":"2024-02-19T10:22:44Z","publication":"International Mathematics Research Notices","external_id":{"arxiv":["1810.12491"]},"title":"Tamely ramified geometric Langlands correspondence in positive characteristic","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1093/imrn/rnae005"}],"project":[{"call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"citation":{"chicago":"Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae005\">https://doi.org/10.1093/imrn/rnae005</a>.","ieee":"S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024.","ista":"Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices.","short":"S. Shen, International Mathematics Research Notices (2024).","mla":"Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” <i>International Mathematics Research Notices</i>, Oxford University Press, 2024, doi:<a href=\"https://doi.org/10.1093/imrn/rnae005\">10.1093/imrn/rnae005</a>.","apa":"Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive characteristic. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae005\">https://doi.org/10.1093/imrn/rnae005</a>","ama":"Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. <i>International Mathematics Research Notices</i>. 2024. doi:<a href=\"https://doi.org/10.1093/imrn/rnae005\">10.1093/imrn/rnae005</a>"},"arxiv":1},{"article_type":"original","volume":30,"isi":1,"publication_identifier":{"eissn":["1945-001X"],"issn":["1073-2780"]},"quality_controlled":"1","month":"06","intvolume":"        30","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","department":[{"_id":"TaHa"}],"date_created":"2023-07-23T22:01:14Z","date_published":"2023-06-21T00:00:00Z","_id":"13268","oa":1,"author":[{"last_name":"Huybrechts","full_name":"Huybrechts, D.","first_name":"D."},{"last_name":"Mauri","id":"2cf70c34-09c1-11ed-bd8d-c34fac206130","first_name":"Mirko","full_name":"Mauri, Mirko"}],"type":"journal_article","year":"2023","publisher":"International Press","doi":"10.4310/mrl.2023.v30.n1.a6","language":[{"iso":"eng"}],"title":"On type II degenerations of hyperkähler manifolds","external_id":{"arxiv":["2108.01587"],"isi":["001027656000006"]},"publication":"Mathematical Research Letters","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.01587","open_access":"1"}],"scopus_import":"1","issue":"1","arxiv":1,"citation":{"ama":"Huybrechts D, Mauri M. On type II degenerations of hyperkähler manifolds. <i>Mathematical Research Letters</i>. 2023;30(1):125-141. doi:<a href=\"https://doi.org/10.4310/mrl.2023.v30.n1.a6\">10.4310/mrl.2023.v30.n1.a6</a>","apa":"Huybrechts, D., &#38; Mauri, M. (2023). On type II degenerations of hyperkähler manifolds. <i>Mathematical Research Letters</i>. International Press. <a href=\"https://doi.org/10.4310/mrl.2023.v30.n1.a6\">https://doi.org/10.4310/mrl.2023.v30.n1.a6</a>","short":"D. Huybrechts, M. Mauri, Mathematical Research Letters 30 (2023) 125–141.","mla":"Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.” <i>Mathematical Research Letters</i>, vol. 30, no. 1, International Press, 2023, pp. 125–41, doi:<a href=\"https://doi.org/10.4310/mrl.2023.v30.n1.a6\">10.4310/mrl.2023.v30.n1.a6</a>.","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,” <i>Mathematical Research Letters</i>, vol. 30, no. 1. International Press, pp. 125–141, 2023.","chicago":"Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.” <i>Mathematical Research Letters</i>. International Press, 2023. <a href=\"https://doi.org/10.4310/mrl.2023.v30.n1.a6\">https://doi.org/10.4310/mrl.2023.v30.n1.a6</a>."},"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"abstract":[{"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.","lang":"eng"}],"ec_funded":1,"day":"21","oa_version":"Preprint","publication_status":"published","page":"125-141","status":"public","date_updated":"2024-01-16T12:00:47Z"},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2203.12666","open_access":"1"}],"external_id":{"arxiv":["2203.12666"]},"title":"Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling","publication":"Physical Review B","project":[{"_id":"26986C82-B435-11E9-9278-68D0E5697425","name":"A path-integral approach to composite impurities","grant_number":"M02641","call_identifier":"FWF"},{"name":"Algebro-Geometric Applications of Factorization Homology","_id":"26B96266-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"M02751"},{"call_identifier":"FWF","grant_number":"P29902","name":"Quantum rotations in the presence of a many-body environment","_id":"26031614-B435-11E9-9278-68D0E5697425"},{"_id":"2688CF98-B435-11E9-9278-68D0E5697425","name":"Angulon: physics and applications of a new quasiparticle","call_identifier":"H2020","grant_number":"801770"}],"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. <i>Physical Review B</i>. 2023;108(4). doi:<a href=\"https://doi.org/10.1103/PhysRevB.108.045115\">10.1103/PhysRevB.108.045115</a>","mla":"Bighin, Giacomo, et al. “Diagrammatic Monte Carlo for Electronic Correlation in Molecules: High-Order Many-Body Perturbation Theory with Low Scaling.” <i>Physical Review B</i>, vol. 108, no. 4, 045115, American Physical Society, 2023, doi:<a href=\"https://doi.org/10.1103/PhysRevB.108.045115\">10.1103/PhysRevB.108.045115</a>.","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.","apa":"Bighin, G., Ho, Q. P., Lemeshko, M., &#38; Tscherbul, T. V. (2023). Diagrammatic Monte Carlo for electronic correlation in molecules: High-order many-body perturbation theory with low scaling. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevB.108.045115\">https://doi.org/10.1103/PhysRevB.108.045115</a>","short":"G. Bighin, Q.P. Ho, M. Lemeshko, T.V. Tscherbul, Physical Review B 108 (2023).","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,” <i>Physical Review B</i>, vol. 108, no. 4. American Physical Society, 2023.","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.” <i>Physical Review B</i>. American Physical Society, 2023. <a href=\"https://doi.org/10.1103/PhysRevB.108.045115\">https://doi.org/10.1103/PhysRevB.108.045115</a>."},"arxiv":1,"issue":"4","scopus_import":"1","ec_funded":1,"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."}],"oa_version":"Preprint","publication_status":"published","day":"15","date_updated":"2024-08-07T07:16:52Z","status":"public","quality_controlled":"1","publication_identifier":{"issn":["2469-9950"],"eissn":["2469-9969"]},"month":"07","article_type":"original","volume":108,"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.","department":[{"_id":"MiLe"},{"_id":"TaHa"}],"date_created":"2023-08-06T22:01:10Z","article_number":"045115","intvolume":"       108","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"_id":"13966","author":[{"first_name":"Giacomo","full_name":"Bighin, Giacomo","orcid":"0000-0001-8823-9777","id":"4CA96FD4-F248-11E8-B48F-1D18A9856A87","last_name":"Bighin"},{"first_name":"Quoc P","full_name":"Ho, Quoc P","last_name":"Ho","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6889-1418"},{"orcid":"0000-0002-6990-7802","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","last_name":"Lemeshko","full_name":"Lemeshko, Mikhail","first_name":"Mikhail"},{"first_name":"T. V.","full_name":"Tscherbul, T. V.","last_name":"Tscherbul"}],"date_published":"2023-07-15T00:00:00Z","publisher":"American Physical Society","year":"2023","language":[{"iso":"eng"}],"doi":"10.1103/PhysRevB.108.045115","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 ."}],"ec_funded":1,"day":"03","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"oa_version":"Published Version","publication_status":"published","date_updated":"2023-12-13T12:18:18Z","status":"public","title":"Homological Bondal-Orlov localization conjecture for rational singularities","file":[{"date_updated":"2023-09-05T06:43:11Z","success":1,"checksum":"c36241750cc5cb06890aec0ecdfee626","date_created":"2023-09-05T06:43:11Z","file_id":"14266","file_size":280865,"file_name":"2023_ForumMathematics_Mauri.pdf","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst"}],"external_id":{"arxiv":["2212.06786"],"isi":["001041926700001"]},"publication":"Forum of Mathematics, Sigma","citation":{"ama":"Mauri M, Shinder E. Homological Bondal-Orlov localization conjecture for rational singularities. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fms.2023.65\">10.1017/fms.2023.65</a>","short":"M. Mauri, E. Shinder, Forum of Mathematics, Sigma 11 (2023).","apa":"Mauri, M., &#38; Shinder, E. (2023). Homological Bondal-Orlov localization conjecture for rational singularities. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.65\">https://doi.org/10.1017/fms.2023.65</a>","mla":"Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e66, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fms.2023.65\">10.1017/fms.2023.65</a>.","ista":"Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 11, e66.","ieee":"M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture for rational singularities,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge University Press, 2023.","chicago":"Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.65\">https://doi.org/10.1017/fms.2023.65</a>."},"arxiv":1,"project":[{"call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"has_accepted_license":"1","scopus_import":"1","_id":"14239","oa":1,"author":[{"first_name":"Mirko","full_name":"Mauri, Mirko","last_name":"Mauri","id":"2cf70c34-09c1-11ed-bd8d-c34fac206130"},{"last_name":"Shinder","full_name":"Shinder, Evgeny","first_name":"Evgeny"}],"date_published":"2023-08-03T00:00:00Z","year":"2023","publisher":"Cambridge University Press","doi":"10.1017/fms.2023.65","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"eissn":["2050-5094"]},"quality_controlled":"1","month":"08","article_type":"original","volume":11,"isi":1,"department":[{"_id":"TaHa"}],"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","date_created":"2023-08-27T22:01:16Z","article_number":"e66","intvolume":"        11","file_date_updated":"2023-09-05T06:43:11Z","article_processing_charge":"Yes","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"]},{"project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces","grant_number":"320593","call_identifier":"FP7"},{"name":"Arithmetic quantization of character and quiver varities","_id":"25E6C798-B435-11E9-9278-68D0E5697425","grant_number":"153627"}],"citation":{"chicago":"Hausel, Tamás, Michael Lennox Wong, and Dimitri Wyss. “Arithmetic and Metric Aspects of Open de Rham Spaces.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2023. <a href=\"https://doi.org/10.1112/plms.12555\">https://doi.org/10.1112/plms.12555</a>.","ieee":"T. Hausel, M. L. Wong, and D. Wyss, “Arithmetic and metric aspects of open de Rham spaces,” <i>Proceedings of the London Mathematical Society</i>, 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.","apa":"Hausel, T., Wong, M. L., &#38; Wyss, D. (2023). Arithmetic and metric aspects of open de Rham spaces. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.12555\">https://doi.org/10.1112/plms.12555</a>","short":"T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society 127 (2023) 958–1027.","mla":"Hausel, Tamás, et al. “Arithmetic and Metric Aspects of Open de Rham Spaces.” <i>Proceedings of the London Mathematical Society</i>, vol. 127, no. 4, Wiley, 2023, pp. 958–1027, doi:<a href=\"https://doi.org/10.1112/plms.12555\">10.1112/plms.12555</a>.","ama":"Hausel T, Wong ML, Wyss D. Arithmetic and metric aspects of open de Rham spaces. <i>Proceedings of the London Mathematical Society</i>. 2023;127(4):958-1027. doi:<a href=\"https://doi.org/10.1112/plms.12555\">10.1112/plms.12555</a>"},"arxiv":1,"issue":"4","scopus_import":"1","has_accepted_license":"1","publication":"Proceedings of the London Mathematical Society","external_id":{"arxiv":["1807.04057"],"isi":["001049312700001"]},"title":"Arithmetic and metric aspects of open de Rham spaces","file":[{"file_name":"2023_ProcLondonMathSoc_Hausel.pdf","file_size":651335,"file_id":"14910","checksum":"2af4d2d6a8ae42f7d3fba0188e79ae82","date_created":"2024-01-30T12:56:00Z","date_updated":"2024-01-30T12:56:00Z","success":1,"creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"date_updated":"2024-01-30T12:56:10Z","status":"public","page":"958-1027","oa_version":"Published Version","publication_status":"published","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ec_funded":1,"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."}],"date_created":"2023-08-27T22:01:18Z","department":[{"_id":"TaHa"}],"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)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"file_date_updated":"2024-01-30T12:56:00Z","intvolume":"       127","month":"10","quality_controlled":"1","publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"isi":1,"article_type":"original","volume":127,"language":[{"iso":"eng"}],"doi":"10.1112/plms.12555","publisher":"Wiley","year":"2023","type":"journal_article","author":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás","full_name":"Hausel, Tamás"},{"full_name":"Wong, Michael Lennox","first_name":"Michael Lennox","last_name":"Wong"},{"first_name":"Dimitri","full_name":"Wyss, Dimitri","last_name":"Wyss"}],"oa":1,"_id":"14244","date_published":"2023-10-01T00:00:00Z"},{"month":"01","publication_identifier":{"eissn":["2045-2322"]},"quality_controlled":"1","isi":1,"volume":13,"article_type":"original","article_number":"468","date_created":"2023-01-22T23:00:55Z","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.","department":[{"_id":"TaHa"}],"file_date_updated":"2023-01-23T07:53:23Z","article_processing_charge":"No","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        13","author":[{"last_name":"Gómez","first_name":"Arturo","full_name":"Gómez, Arturo"},{"full_name":"Oliveira, Goncalo","first_name":"Goncalo","id":"58abbde8-f455-11eb-a497-98c8fd71b905","last_name":"Oliveira"}],"_id":"12329","oa":1,"date_published":"2023-01-10T00:00:00Z","doi":"10.1038/s41598-022-19827-9","language":[{"iso":"eng"}],"year":"2023","publisher":"Springer Nature","type":"journal_article","publication":"Scientific Reports","file":[{"date_updated":"2023-01-23T07:53:23Z","success":1,"checksum":"a8b83739f4a951e83e0b2a778f03b327","file_id":"12336","date_created":"2023-01-23T07:53:23Z","file_size":2167792,"file_name":"2023_ScientificReports_Gomez.pdf","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst"}],"title":"New approaches to epidemic modeling on networks","external_id":{"isi":["001003345000051"]},"citation":{"apa":"Gómez, A., &#38; Oliveira, G. (2023). New approaches to epidemic modeling on networks. <i>Scientific Reports</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41598-022-19827-9\">https://doi.org/10.1038/s41598-022-19827-9</a>","short":"A. Gómez, G. Oliveira, Scientific Reports 13 (2023).","mla":"Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on Networks.” <i>Scientific Reports</i>, vol. 13, 468, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1038/s41598-022-19827-9\">10.1038/s41598-022-19827-9</a>.","ista":"Gómez A, Oliveira G. 2023. New approaches to epidemic modeling on networks. Scientific Reports. 13, 468.","ama":"Gómez A, Oliveira G. New approaches to epidemic modeling on networks. <i>Scientific Reports</i>. 2023;13. doi:<a href=\"https://doi.org/10.1038/s41598-022-19827-9\">10.1038/s41598-022-19827-9</a>","chicago":"Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on Networks.” <i>Scientific Reports</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1038/s41598-022-19827-9\">https://doi.org/10.1038/s41598-022-19827-9</a>.","ieee":"A. Gómez and G. Oliveira, “New approaches to epidemic modeling on networks,” <i>Scientific Reports</i>, vol. 13. Springer Nature, 2023."},"scopus_import":"1","has_accepted_license":"1","day":"10","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication_status":"published","oa_version":"Published Version","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"}],"date_updated":"2023-08-01T12:31:40Z","status":"public"},{"external_id":{"arxiv":["2101.08583"],"isi":["000745495400001"]},"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/"}]},"title":"Very stable Higgs bundles, equivariant multiplicity and mirror symmetry","file":[{"success":1,"date_updated":"2023-02-27T07:30:47Z","date_created":"2023-02-27T07:30:47Z","file_id":"12687","checksum":"a382ba75acebc9adfb8fe56247cb410e","file_size":1069538,"file_name":"2022_InventionesMahtematicae_Hausel.pdf","content_type":"application/pdf","relation":"main_file","access_level":"open_access","creator":"dernst"}],"publication":"Inventiones Mathematicae","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"citation":{"ama":"Hausel T, Hitchin N. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. <i>Inventiones Mathematicae</i>. 2022;228:893-989. doi:<a href=\"https://doi.org/10.1007/s00222-021-01093-7\">10.1007/s00222-021-01093-7</a>","ista":"Hausel T, Hitchin N. 2022. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. Inventiones Mathematicae. 228, 893–989.","short":"T. Hausel, N. Hitchin, Inventiones Mathematicae 228 (2022) 893–989.","mla":"Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” <i>Inventiones Mathematicae</i>, vol. 228, Springer Nature, 2022, pp. 893–989, doi:<a href=\"https://doi.org/10.1007/s00222-021-01093-7\">10.1007/s00222-021-01093-7</a>.","apa":"Hausel, T., &#38; Hitchin, N. (2022). Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-021-01093-7\">https://doi.org/10.1007/s00222-021-01093-7</a>","ieee":"T. Hausel and N. Hitchin, “Very stable Higgs bundles, equivariant multiplicity and mirror symmetry,” <i>Inventiones Mathematicae</i>, vol. 228. Springer Nature, pp. 893–989, 2022.","chicago":"Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity and Mirror Symmetry.” <i>Inventiones Mathematicae</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00222-021-01093-7\">https://doi.org/10.1007/s00222-021-01093-7</a>."},"arxiv":1,"has_accepted_license":"1","scopus_import":"1","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."}],"page":"893-989","oa_version":"Published Version","publication_status":"published","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","date_updated":"2023-08-02T14:03:20Z","status":"public","quality_controlled":"1","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"month":"05","article_type":"original","volume":228,"isi":1,"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).","department":[{"_id":"TaHa"}],"date_created":"2022-01-30T23:01:34Z","intvolume":"       228","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2023-02-27T07:30:47Z","oa":1,"_id":"10704","author":[{"full_name":"Hausel, Tamás","first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"},{"last_name":"Hitchin","full_name":"Hitchin, Nigel","first_name":"Nigel"}],"date_published":"2022-05-01T00:00:00Z","publisher":"Springer Nature","year":"2022","language":[{"iso":"eng"}],"doi":"10.1007/s00222-021-01093-7","type":"journal_article"},{"isi":1,"article_type":"original","volume":105,"month":"02","quality_controlled":"1","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"article_processing_charge":"Yes (via OA deal)","file_date_updated":"2022-02-21T11:22:58Z","intvolume":"       105","date_created":"2022-02-20T23:01:33Z","department":[{"_id":"TaHa"}],"acknowledgement":"This paper is based on my PhD thesis, which would not be possible without the support of my advisor Bernd Siebert. I also thank Dan Abramovich, Mohammed Abouzaid, Mark Gross, Tom Coates and Dimitri Zvonkine for many useful conversations. Finally, I thank the anonymous referees for their many insightful comments and valuable suggestions which have resulted in major improvements to this article. This project has received funding from the EuropeanResearch Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement Number: 682603), and from Fondation Mathématique Jacques Hadamard. ","date_published":"2022-02-05T00:00:00Z","author":[{"first_name":"Nuroemuer Huelya","full_name":"Arguez, Nuroemuer Huelya","last_name":"Arguez","id":"3c26b22e-c843-11eb-aa56-d38ffa0bdd08"}],"oa":1,"_id":"10772","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1112/jlms.12515","publisher":"London Mathematical Society","year":"2022","publication":"Journal of the London Mathematical Society","external_id":{"arxiv":["1712.10260"],"isi":["000751600600001"]},"title":"Mirror symmetry for the Tate curve via tropical and log corals","file":[{"file_name":"2022_JournLondonMathSociety_Arguez.pdf","file_size":936873,"file_id":"10783","checksum":"8bd0fd9694be894a191857ddf27678f0","date_created":"2022-02-21T11:22:58Z","success":1,"date_updated":"2022-02-21T11:22:58Z","creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file"}],"issue":"1","scopus_import":"1","has_accepted_license":"1","citation":{"chicago":"Arguez, Nuroemuer Huelya. “Mirror Symmetry for the Tate Curve via Tropical and Log Corals.” <i>Journal of the London Mathematical Society</i>. London Mathematical Society, 2022. <a href=\"https://doi.org/10.1112/jlms.12515\">https://doi.org/10.1112/jlms.12515</a>.","ieee":"N. H. Arguez, “Mirror symmetry for the Tate curve via tropical and log corals,” <i>Journal of the London Mathematical Society</i>, vol. 105, no. 1. London Mathematical Society, pp. 343–411, 2022.","ista":"Arguez NH. 2022. Mirror symmetry for the Tate curve via tropical and log corals. Journal of the London Mathematical Society. 105(1), 343–411.","apa":"Arguez, N. H. (2022). Mirror symmetry for the Tate curve via tropical and log corals. <i>Journal of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/jlms.12515\">https://doi.org/10.1112/jlms.12515</a>","short":"N.H. Arguez, Journal of the London Mathematical Society 105 (2022) 343–411.","mla":"Arguez, Nuroemuer Huelya. “Mirror Symmetry for the Tate Curve via Tropical and Log Corals.” <i>Journal of the London Mathematical Society</i>, vol. 105, no. 1, London Mathematical Society, 2022, pp. 343–411, doi:<a href=\"https://doi.org/10.1112/jlms.12515\">10.1112/jlms.12515</a>.","ama":"Arguez NH. Mirror symmetry for the Tate curve via tropical and log corals. <i>Journal of the London Mathematical Society</i>. 2022;105(1):343-411. doi:<a href=\"https://doi.org/10.1112/jlms.12515\">10.1112/jlms.12515</a>"},"arxiv":1,"oa_version":"Published Version","publication_status":"published","page":"343-411","tmp":{"image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"day":"05","abstract":[{"lang":"eng","text":"We introduce tropical corals, balanced trees in a half-space, and show that they correspond to holomorphic polygons capturing the product rule in Lagrangian Floer theory for the elliptic curve. We then prove a correspondence theorem equating counts of tropical corals to punctured log Gromov–Witten invariants of the Tate curve. This implies that the homogeneous coordinate ring of the mirror to the Tate curve is isomorphic to the degree-zero part of symplectic cohomology, confirming a prediction of homological mirror symmetry."}],"status":"public","date_updated":"2023-08-02T14:29:50Z"},{"abstract":[{"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).","lang":"eng"}],"edition":"1","ec_funded":1,"day":"16","oa_version":"Preprint","page":"347-392","publication_status":"published","date_updated":"2023-01-27T07:07:31Z","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1810.10095"}],"title":"Loop Grassmannians of Quivers and Affine Quantum Groups","external_id":{"arxiv":["1810.10095"]},"series_title":"TM","publication":"Representation Theory and Algebraic Geometry","citation":{"ieee":"I. Mirković, Y. Yang, and G. Zhao, “Loop Grassmannians of Quivers and Affine Quantum Groups,” in <i>Representation Theory and Algebraic Geometry</i>, 1st ed., V. Baranovskky, N. Guay, and T. Schedler, Eds. Cham: Springer Nature; Birkhäuser, 2022, pp. 347–392.","chicago":"Mirković, Ivan, Yaping Yang, and Gufang Zhao. “Loop Grassmannians of Quivers and Affine Quantum Groups.” In <i>Representation Theory and Algebraic Geometry</i>, edited by Vladimir Baranovskky, Nicolas Guay, and Travis Schedler, 1st ed., 347–92. TM. Cham: Springer Nature; Birkhäuser, 2022. <a href=\"https://doi.org/10.1007/978-3-030-82007-7_8\">https://doi.org/10.1007/978-3-030-82007-7_8</a>.","ama":"Mirković I, Yang Y, Zhao G. Loop Grassmannians of Quivers and Affine Quantum Groups. In: Baranovskky V, Guay N, Schedler T, eds. <i>Representation Theory and Algebraic Geometry</i>. 1st ed. TM. Cham: Springer Nature; Birkhäuser; 2022:347-392. doi:<a href=\"https://doi.org/10.1007/978-3-030-82007-7_8\">10.1007/978-3-030-82007-7_8</a>","mla":"Mirković, Ivan, et al. “Loop Grassmannians of Quivers and Affine Quantum Groups.” <i>Representation Theory and Algebraic Geometry</i>, edited by Vladimir Baranovskky et al., 1st ed., Springer Nature; Birkhäuser, 2022, pp. 347–92, doi:<a href=\"https://doi.org/10.1007/978-3-030-82007-7_8\">10.1007/978-3-030-82007-7_8</a>.","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.","apa":"Mirković, I., Yang, Y., &#38; Zhao, G. (2022). Loop Grassmannians of Quivers and Affine Quantum Groups. In V. Baranovskky, N. Guay, &#38; T. Schedler (Eds.), <i>Representation Theory and Algebraic Geometry</i> (1st ed., pp. 347–392). Cham: Springer Nature; Birkhäuser. <a href=\"https://doi.org/10.1007/978-3-030-82007-7_8\">https://doi.org/10.1007/978-3-030-82007-7_8</a>","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."},"arxiv":1,"project":[{"call_identifier":"FP7","grant_number":"320593","name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425"}],"alternative_title":["Trends in Mathematics"],"editor":[{"first_name":"Vladimir","full_name":"Baranovskky, Vladimir","last_name":"Baranovskky"},{"last_name":"Guay","first_name":"Nicolas","full_name":"Guay, Nicolas"},{"first_name":"Travis","full_name":"Schedler, Travis","last_name":"Schedler"}],"scopus_import":"1","_id":"12303","oa":1,"author":[{"last_name":"Mirković","first_name":"Ivan","full_name":"Mirković, Ivan"},{"last_name":"Yang","full_name":"Yang, Yaping","first_name":"Yaping"},{"last_name":"Zhao","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","full_name":"Zhao, Gufang","first_name":"Gufang"}],"date_published":"2022-06-16T00:00:00Z","year":"2022","publisher":"Springer Nature; Birkhäuser","doi":"10.1007/978-3-030-82007-7_8","language":[{"iso":"eng"}],"type":"book_chapter","publication_identifier":{"issn":["2297-0215"],"isbn":["9783030820060"],"eisbn":["9783030820077"],"eissn":["2297-024X"]},"quality_controlled":"1","month":"06","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.","department":[{"_id":"TaHa"}],"date_created":"2023-01-16T10:06:41Z","place":"Cham","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No"},{"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.2140/pjm.2022.321.193","publisher":"Mathematical Sciences Publishers","year":"2022","date_published":"2022-08-29T00:00:00Z","author":[{"last_name":"Yu","id":"3D7DD9BE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5128-7126","full_name":"Yu, Hongjie","first_name":"Hongjie"}],"oa":1,"_id":"12793","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","keyword":["Arthur–Selberg trace formula","cuspidal automorphic representations","global function fields"],"intvolume":"       321","date_created":"2023-04-02T22:01:11Z","department":[{"_id":"TaHa"}],"acknowledgement":"I’d like to thank Prof. Chaudouard for introducing me to this area. I’d like to thank Prof. Harris for asking me the question that makes Section 10 possible. I’m grateful for the support of Prof. Hausel and IST Austria. The author was funded by an ISTplus fellowship: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","isi":1,"volume":321,"article_type":"original","month":"08","quality_controlled":"1","publication_identifier":{"issn":["0030-8730"],"eissn":["1945-5844"]},"status":"public","date_updated":"2023-08-04T10:42:38Z","publication_status":"published","page":"193-237","oa_version":"Preprint","day":"29","ec_funded":1,"abstract":[{"lang":"eng","text":"Let F be a global function field with constant field Fq. Let G be a reductive group over Fq. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original construction. We establish a coarse geometric expansion for our variant truncation.\r\nAs applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line P1Fq with two points of ramifications."}],"issue":"1","scopus_import":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"}],"citation":{"chicago":"Yu, Hongjie. “ A Coarse Geometric Expansion of a Variant of Arthur’s Truncated Traces and Some Applications.” <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers, 2022. <a href=\"https://doi.org/10.2140/pjm.2022.321.193\">https://doi.org/10.2140/pjm.2022.321.193</a>.","ieee":"H. Yu, “ A coarse geometric expansion of a variant of Arthur’s truncated traces and some applications,” <i>Pacific Journal of Mathematics</i>, vol. 321, no. 1. Mathematical Sciences Publishers, pp. 193–237, 2022.","ista":"Yu H. 2022.  A coarse geometric expansion of a variant of Arthur’s truncated traces and some applications. Pacific Journal of Mathematics. 321(1), 193–237.","apa":"Yu, H. (2022).  A coarse geometric expansion of a variant of Arthur’s truncated traces and some applications. <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pjm.2022.321.193\">https://doi.org/10.2140/pjm.2022.321.193</a>","mla":"Yu, Hongjie. “ A Coarse Geometric Expansion of a Variant of Arthur’s Truncated Traces and Some Applications.” <i>Pacific Journal of Mathematics</i>, vol. 321, no. 1, Mathematical Sciences Publishers, 2022, pp. 193–237, doi:<a href=\"https://doi.org/10.2140/pjm.2022.321.193\">10.2140/pjm.2022.321.193</a>.","short":"H. Yu, Pacific Journal of Mathematics 321 (2022) 193–237.","ama":"Yu H.  A coarse geometric expansion of a variant of Arthur’s truncated traces and some applications. <i>Pacific Journal of Mathematics</i>. 2022;321(1):193-237. doi:<a href=\"https://doi.org/10.2140/pjm.2022.321.193\">10.2140/pjm.2022.321.193</a>"},"arxiv":1,"publication":"Pacific Journal of Mathematics","external_id":{"isi":["000954466300006"],"arxiv":["2109.10245"]},"title":" A coarse geometric expansion of a variant of Arthur's truncated traces and some applications","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2109.10245","open_access":"1"}]},{"title":"Resurgence analysis of quantum invariants of Seifert fibered homology spheres","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","creator":"dernst","success":1,"date_updated":"2022-03-24T11:42:25Z","checksum":"9c72327d39f34f1a6eaa98fa4b8493f2","file_id":"10917","date_created":"2022-03-24T11:42:25Z","file_size":649130,"file_name":"2022_JourLondonMathSoc_Andersen.pdf"}],"external_id":{"isi":["000755205700001"],"arxiv":["1811.05376"]},"publication":"Journal of the London Mathematical Society","has_accepted_license":"1","scopus_import":"1","issue":"2","arxiv":1,"citation":{"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.","apa":"Mistegaard, W., &#38; Andersen, J. E. (2022). Resurgence analysis of quantum invariants of Seifert fibered homology spheres. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.12506\">https://doi.org/10.1112/jlms.12506</a>","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.” <i>Journal of the London Mathematical Society</i>, vol. 105, no. 2, Wiley, 2022, pp. 709–64, doi:<a href=\"https://doi.org/10.1112/jlms.12506\">10.1112/jlms.12506</a>.","ama":"Mistegaard W, Andersen JE. Resurgence analysis of quantum invariants of Seifert fibered homology spheres. <i>Journal of the London Mathematical Society</i>. 2022;105(2):709-764. doi:<a href=\"https://doi.org/10.1112/jlms.12506\">10.1112/jlms.12506</a>","chicago":"Mistegaard, William, and Jørgen Ellegaard Andersen. “Resurgence Analysis of Quantum Invariants of Seifert Fibered Homology Spheres.” <i>Journal of the London Mathematical Society</i>. Wiley, 2022. <a href=\"https://doi.org/10.1112/jlms.12506\">https://doi.org/10.1112/jlms.12506</a>.","ieee":"W. Mistegaard and J. E. Andersen, “Resurgence analysis of quantum invariants of Seifert fibered homology spheres,” <i>Journal of the London Mathematical Society</i>, vol. 105, no. 2. Wiley, pp. 709–764, 2022."},"project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"}],"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."}],"ec_funded":1,"day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"oa_version":"Published Version","page":"709-764","publication_status":"published","status":"public","date_updated":"2023-08-02T06:53:51Z","article_type":"original","volume":105,"isi":1,"publication_identifier":{"eissn":["1469-7750"]},"quality_controlled":"1","month":"03","intvolume":"       105","file_date_updated":"2022-03-24T11:42:25Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"department":[{"_id":"TaHa"}],"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_created":"2021-08-31T12:51:40Z","date_published":"2022-03-01T00:00:00Z","_id":"9977","oa":1,"author":[{"id":"41B03CD0-62AE-11E9-84EF-0718E6697425","last_name":"Mistegaard","full_name":"Mistegaard, William","first_name":"William"},{"last_name":"Andersen","first_name":"Jørgen Ellegaard","full_name":"Andersen, Jørgen Ellegaard"}],"type":"journal_article","year":"2022","publisher":"Wiley","doi":"10.1112/jlms.12506","language":[{"iso":"eng"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","intvolume":"        53","date_created":"2019-10-24T08:04:09Z","department":[{"_id":"TaHa"}],"isi":1,"volume":53,"article_type":"original","month":"04","publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"quality_controlled":"1","type":"journal_article","doi":"10.1112/blms.12442","language":[{"iso":"eng"}],"year":"2021","publisher":"Wiley","date_published":"2021-04-01T00:00:00Z","author":[{"first_name":"Kamil P","full_name":"Rychlewicz, Kamil P","last_name":"Rychlewicz","id":"85A07246-A8BF-11E9-B4FA-D9E3E5697425"}],"_id":"6965","oa":1,"scopus_import":"1","issue":"2","citation":{"chicago":"Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2021. <a href=\"https://doi.org/10.1112/blms.12442\">https://doi.org/10.1112/blms.12442</a>.","ieee":"K. P. Rychlewicz, “The positivity of local equivariant Hirzebruch class for toric varieties,” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2. Wiley, pp. 560–574, 2021.","short":"K.P. Rychlewicz, Bulletin of the London Mathematical Society 53 (2021) 560–574.","ista":"Rychlewicz KP. 2021. The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society. 53(2), 560–574.","mla":"Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2, Wiley, 2021, pp. 560–74, doi:<a href=\"https://doi.org/10.1112/blms.12442\">10.1112/blms.12442</a>.","apa":"Rychlewicz, K. P. (2021). The positivity of local equivariant Hirzebruch class for toric varieties. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12442\">https://doi.org/10.1112/blms.12442</a>","ama":"Rychlewicz KP. The positivity of local equivariant Hirzebruch class for toric varieties. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):560-574. doi:<a href=\"https://doi.org/10.1112/blms.12442\">10.1112/blms.12442</a>"},"arxiv":1,"publication":"Bulletin of the London Mathematical Society","title":"The positivity of local equivariant Hirzebruch class for toric varieties","external_id":{"arxiv":["1910.10435"],"isi":["000594805800001"]},"main_file_link":[{"url":"https://arxiv.org/abs/1910.10435","open_access":"1"}],"status":"public","date_updated":"2023-08-04T10:43:39Z","day":"01","publication_status":"published","oa_version":"Preprint","page":"560-574","abstract":[{"lang":"eng","text":"The central object of investigation of this paper is the Hirzebruch class, a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following the work of Weber, we investigate its equivariant version for (possibly singular) toric varieties. The local decomposition of the Hirzebruch class to the fixed points of the torus action and a formula for the local class in terms of the defining fan are recalled. After this review part, we prove the positivity of local Hirzebruch classes for all toric varieties, thus proving false the alleged counterexample given by Weber."}]},{"intvolume":"       116","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"TaHa"}],"acknowledgement":"I would like to thank Piotr Achinger, Daniel Huybrechts, Katrina Honigs, Marcin Lara, and Maciek Zdanowicz for the mathematical discussions, Tamas Hausel for hosting me in his research group at IST Austria, and the referees for their valuable suggestions. This research has received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie Grant Agreement No. 754411.","date_created":"2021-02-07T23:01:13Z","article_type":"original","volume":116,"isi":1,"publication_identifier":{"issn":["0003889X"],"eissn":["14208938"]},"quality_controlled":"1","month":"05","type":"journal_article","year":"2021","publisher":"Springer Nature","doi":"10.1007/s00013-020-01564-y","language":[{"iso":"eng"}],"date_published":"2021-05-01T00:00:00Z","_id":"9099","oa":1,"author":[{"last_name":"Srivastava","id":"4D046628-F248-11E8-B48F-1D18A9856A87","first_name":"Tanya K","full_name":"Srivastava, Tanya K"}],"scopus_import":"1","issue":"5","arxiv":1,"citation":{"ama":"Srivastava TK. Lifting automorphisms on Abelian varieties as derived autoequivalences. <i>Archiv der Mathematik</i>. 2021;116(5):515-527. doi:<a href=\"https://doi.org/10.1007/s00013-020-01564-y\">10.1007/s00013-020-01564-y</a>","mla":"Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences.” <i>Archiv Der Mathematik</i>, vol. 116, no. 5, Springer Nature, 2021, pp. 515–27, doi:<a href=\"https://doi.org/10.1007/s00013-020-01564-y\">10.1007/s00013-020-01564-y</a>.","apa":"Srivastava, T. K. (2021). Lifting automorphisms on Abelian varieties as derived autoequivalences. <i>Archiv Der Mathematik</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00013-020-01564-y\">https://doi.org/10.1007/s00013-020-01564-y</a>","ista":"Srivastava TK. 2021. Lifting automorphisms on Abelian varieties as derived autoequivalences. Archiv der Mathematik. 116(5), 515–527.","short":"T.K. Srivastava, Archiv Der Mathematik 116 (2021) 515–527.","ieee":"T. K. Srivastava, “Lifting automorphisms on Abelian varieties as derived autoequivalences,” <i>Archiv der Mathematik</i>, vol. 116, no. 5. Springer Nature, pp. 515–527, 2021.","chicago":"Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences.” <i>Archiv Der Mathematik</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00013-020-01564-y\">https://doi.org/10.1007/s00013-020-01564-y</a>."},"project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"}],"title":"Lifting automorphisms on Abelian varieties as derived autoequivalences","external_id":{"arxiv":["2001.07762"],"isi":["000612580200001"]},"publication":"Archiv der Mathematik","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.07762"}],"status":"public","date_updated":"2023-08-07T13:42:38Z","abstract":[{"text":"We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to a field of characteristic zero as a morphism vanishes if and only if it vanishes for lifting it as a derived autoequivalence. We also compare the deformation space of these two types of deformations.","lang":"eng"}],"ec_funded":1,"day":"01","oa_version":"Preprint","page":"515-527","publication_status":"published"},{"type":"journal_article","publisher":"Elsevier","year":"2021","language":[{"iso":"eng"}],"doi":"10.1016/j.bulsci.2021.102957","date_published":"2021-03-01T00:00:00Z","oa":1,"_id":"9173","author":[{"id":"4D046628-F248-11E8-B48F-1D18A9856A87","last_name":"Srivastava","full_name":"Srivastava, Tanya K","first_name":"Tanya K"}],"intvolume":"       167","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","department":[{"_id":"TaHa"}],"acknowledgement":"I would like to thank M. Zdanwociz for various mathematical discussions which lead to this article, Tamas Hausel for hosting me in his research group at IST Austria and the anonymous referee for their helpful suggestions and comments. This research has received funding from the European Union's Horizon 2020 Marie Sklodowska-Curie Actions Grant No. 754411 and Institue of Science and Technology Austria IST-PLUS Grant No. 754411.","date_created":"2021-02-21T23:01:20Z","article_number":"102957","article_type":"original","volume":167,"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["0007-4497"]},"month":"03","status":"public","date_updated":"2023-08-07T13:47:48Z","ec_funded":1,"abstract":[{"lang":"eng","text":"We show that Hilbert schemes of points on supersingular Enriques surface in characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties but are not irreducible symplectic as the hodge number h2,0 > 1, even though a supersingular Enriques surface is an irreducible symplectic variety. These are the classes of varieties which appear only in characteristic 2 and they show that the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor Calabi-Yau, thereby showing that there are strictly more classes of simply connected varieties with trivial canonical class in characteristic 2 than over C as given by Beauville-Bogolomov decomposition theorem."}],"oa_version":"Preprint","publication_status":"published","day":"01","issue":"03","scopus_import":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"}],"citation":{"ieee":"T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular Enriques surface,” <i>Bulletin des Sciences Mathematiques</i>, vol. 167, no. 03. Elsevier, 2021.","chicago":"Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” <i>Bulletin Des Sciences Mathematiques</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.bulsci.2021.102957\">https://doi.org/10.1016/j.bulsci.2021.102957</a>.","ama":"Srivastava TK. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. <i>Bulletin des Sciences Mathematiques</i>. 2021;167(03). doi:<a href=\"https://doi.org/10.1016/j.bulsci.2021.102957\">10.1016/j.bulsci.2021.102957</a>","mla":"Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” <i>Bulletin Des Sciences Mathematiques</i>, vol. 167, no. 03, 102957, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.bulsci.2021.102957\">10.1016/j.bulsci.2021.102957</a>.","short":"T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021).","apa":"Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. <i>Bulletin Des Sciences Mathematiques</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.bulsci.2021.102957\">https://doi.org/10.1016/j.bulsci.2021.102957</a>","ista":"Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957."},"arxiv":1,"external_id":{"isi":["000623881600009"],"arxiv":["2010.08976"]},"title":"Pathologies of the Hilbert scheme of points of a supersingular Enriques surface","publication":"Bulletin des Sciences Mathematiques","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2010.08976"}]},{"status":"public","date_updated":"2023-08-08T13:28:59Z","ec_funded":1,"abstract":[{"text":"We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras, we obtain new expressions for the cohomologies of the latter. As a consequence, we obtain a uniform and conceptual approach for treating homological stability, homological densities, and arithmetic densities of generalized configuration spaces. Our results categorify, generalize, and in fact provide a conceptual understanding of the coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of the stable homological densities also yields rational homotopy types, answering a question posed by Vakil--Wood. Our approach hinges on the study of homological stability of cohomological Chevalley complexes, which is of independent interest.\r\n","lang":"eng"}],"page":"813-912","oa_version":"Submitted Version","publication_status":"published","day":"27","has_accepted_license":"1","issue":"2","project":[{"call_identifier":"FP7","grant_number":"320593","_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces"},{"_id":"26B96266-B435-11E9-9278-68D0E5697425","name":"Algebro-Geometric Applications of Factorization Homology","grant_number":"M02751","call_identifier":"FWF"}],"citation":{"chicago":"Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” <i>Geometry &#38; Topology</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/gt.2021.25.813\">https://doi.org/10.2140/gt.2021.25.813</a>.","ieee":"Q. P. Ho, “Homological stability and densities of generalized configuration spaces,” <i>Geometry &#38; Topology</i>, vol. 25, no. 2. Mathematical Sciences Publishers, pp. 813–912, 2021.","ista":"Ho QP. 2021. Homological stability and densities of generalized configuration spaces. Geometry &#38; Topology. 25(2), 813–912.","mla":"Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” <i>Geometry &#38; Topology</i>, vol. 25, no. 2, Mathematical Sciences Publishers, 2021, pp. 813–912, doi:<a href=\"https://doi.org/10.2140/gt.2021.25.813\">10.2140/gt.2021.25.813</a>.","apa":"Ho, Q. P. (2021). Homological stability and densities of generalized configuration spaces. <i>Geometry &#38; Topology</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/gt.2021.25.813\">https://doi.org/10.2140/gt.2021.25.813</a>","short":"Q.P. Ho, Geometry &#38; Topology 25 (2021) 813–912.","ama":"Ho QP. Homological stability and densities of generalized configuration spaces. <i>Geometry &#38; Topology</i>. 2021;25(2):813-912. doi:<a href=\"https://doi.org/10.2140/gt.2021.25.813\">10.2140/gt.2021.25.813</a>"},"arxiv":1,"external_id":{"arxiv":["1802.07948"],"isi":["000682738600005"]},"file":[{"success":1,"date_updated":"2021-05-03T06:54:06Z","date_created":"2021-05-03T06:54:06Z","checksum":"643a8d2d6f06f0888dcd7503f55d0920","file_id":"9366","file_size":479268,"file_name":"densities.pdf","content_type":"application/pdf","relation":"main_file","access_level":"open_access","creator":"qho"}],"title":"Homological stability and densities of generalized configuration spaces","publication":"Geometry & Topology","type":"journal_article","publisher":"Mathematical Sciences Publishers","year":"2021","language":[{"iso":"eng"}],"doi":"10.2140/gt.2021.25.813","date_published":"2021-04-27T00:00:00Z","oa":1,"_id":"9359","author":[{"full_name":"Ho, Quoc P","first_name":"Quoc P","last_name":"Ho","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87"}],"keyword":["Generalized configuration spaces","homological stability","homological densities","chiral algebras","chiral homology","factorization algebras","Koszul duality","Ran space"],"intvolume":"        25","ddc":["514","516","512"],"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2021-05-03T06:54:06Z","acknowledgement":"This paper owes an obvious intellectual debt to the illuminating treatments of factorization homology by J.\r\nFrancis, D. Gaitsgory, and J. Lurie in [GL,G1, FG]. The author would like to thank B. Farb and J. Wolfson for\r\nbringing the question of explaining coincidences in homological densities to his attention. Moreover, the author\r\nthanks J. Wolfson for many helpful conversations on the subject, O. Randal-Williams for many comments which\r\ngreatly help improve the exposition, and G. C. Drummond-Cole for many useful conversations on L∞-algebras.\r\nFinally, the author is grateful to the anonymous referee for carefully reading the manuscript and for providing\r\nnumerous comments which greatly helped improve the clarity and precision of the exposition.\r\nThis work is supported by the Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 of\r\nthe European Research Council and the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization\r\nHomology,” Austrian Science Fund (FWF): M 2751.","department":[{"_id":"TaHa"}],"date_created":"2021-05-02T06:59:33Z","article_type":"original","volume":25,"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["1364-0380"]},"month":"04"},{"date_updated":"2023-08-14T06:54:35Z","status":"public","abstract":[{"text":"The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5].","lang":"eng"}],"day":"21","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication_status":"published","oa_version":"Published Version","citation":{"ieee":"Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” <i>Advances in Mathematics</i>, vol. 392. Elsevier, 2021.","chicago":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>.","ama":"Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. 2021;392. doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>","apa":"Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>","ista":"Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992.","mla":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>, vol. 392, 107992, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>.","short":"Q.P. Ho, Advances in Mathematics 392 (2021)."},"arxiv":1,"project":[{"name":"Algebro-Geometric Applications of Factorization Homology","_id":"26B96266-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"M02751"}],"has_accepted_license":"1","scopus_import":"1","title":"The Atiyah-Bott formula and connectivity in chiral Koszul duality","file":[{"creator":"qho","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_name":"1-s2.0-S000187082100431X-main.pdf","file_size":840635,"checksum":"f3c0086d41af11db31c00014efb38072","date_created":"2021-09-21T15:58:52Z","file_id":"10034","date_updated":"2021-09-21T15:58:52Z"}],"external_id":{"isi":["000707040300031"],"arxiv":["1610.00212"]},"publication":"Advances in Mathematics","year":"2021","publisher":"Elsevier","doi":"10.1016/j.aim.2021.107992","language":[{"iso":"eng"}],"type":"journal_article","_id":"10033","oa":1,"author":[{"id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","last_name":"Ho","orcid":"0000-0001-6889-1418","full_name":"Ho, Quoc P","first_name":"Quoc P"}],"date_published":"2021-09-21T00:00:00Z","department":[{"_id":"TaHa"}],"acknowledgement":"The author would like to express his gratitude to D. Gaitsgory, without whose tireless guidance and encouragement in pursuing this problem, this work would not have been possible. The author is grateful to his advisor B.C. Ngô for many years of patient guidance and support. This paper is revised while the author is a postdoc in Hausel group at IST Austria. We thank him and the group for providing a wonderful research environment. The author also gratefully acknowledges the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization Homology,” Austrian Science Fund (FWF): M 2751.","article_number":"107992","date_created":"2021-09-21T15:58:59Z","intvolume":"       392","keyword":["Chiral algebras","Chiral homology","Factorization algebras","Koszul duality","Ran space"],"file_date_updated":"2021-09-21T15:58:52Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","ddc":["514"],"publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"quality_controlled":"1","month":"09","article_type":"original","volume":392,"isi":1},{"publication":"Selecta Mathematica","external_id":{"isi":["000692795200001"]},"file":[{"creator":"cchlebak","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":584648,"file_name":"2021_SelectaMath_Koroteev.pdf","success":1,"date_updated":"2021-09-13T11:31:34Z","checksum":"beadc5a722ffb48190e1e63ee2dbfee5","file_id":"10010","date_created":"2021-09-13T11:31:34Z"}],"title":"Quantum K-theory of quiver varieties and many-body systems","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"citation":{"ama":"Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. Quantum K-theory of quiver varieties and many-body systems. <i>Selecta Mathematica</i>. 2021;27(5). doi:<a href=\"https://doi.org/10.1007/s00029-021-00698-3\">10.1007/s00029-021-00698-3</a>","short":"P. Koroteev, P. Pushkar, A.V. Smirnov, A.M. Zeitlin, Selecta Mathematica 27 (2021).","mla":"Koroteev, Peter, et al. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” <i>Selecta Mathematica</i>, vol. 27, no. 5, 87, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00029-021-00698-3\">10.1007/s00029-021-00698-3</a>.","ista":"Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. 2021. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 27(5), 87.","apa":"Koroteev, P., Pushkar, P., Smirnov, A. V., &#38; Zeitlin, A. M. (2021). Quantum K-theory of quiver varieties and many-body systems. <i>Selecta Mathematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00029-021-00698-3\">https://doi.org/10.1007/s00029-021-00698-3</a>","ieee":"P. Koroteev, P. Pushkar, A. V. Smirnov, and A. M. Zeitlin, “Quantum K-theory of quiver varieties and many-body systems,” <i>Selecta Mathematica</i>, vol. 27, no. 5. Springer Nature, 2021.","chicago":"Koroteev, Peter, Petr Pushkar, Andrey V. Smirnov, and Anton M. Zeitlin. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” <i>Selecta Mathematica</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00029-021-00698-3\">https://doi.org/10.1007/s00029-021-00698-3</a>."},"issue":"5","scopus_import":"1","has_accepted_license":"1","oa_version":"Published Version","publication_status":"published","day":"30","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice."}],"date_updated":"2023-08-14T06:34:14Z","status":"public","month":"08","quality_controlled":"1","publication_identifier":{"eissn":["1420-9020"],"issn":["1022-1824"]},"isi":1,"article_type":"original","volume":27,"date_created":"2021-09-12T22:01:22Z","article_number":"87","acknowledgement":"First of all we would like to thank Andrei Okounkov for invaluable discussions, advises and sharing with us his fantastic viewpoint on modern quantum geometry. We are also grateful to D. Korb and Z. Zhou for their interest and comments. The work of A. Smirnov was supported in part by RFBR Grants under Numbers 15-02-04175 and 15-01-04217 and in part by NSF Grant DMS–2054527. The work of P. Koroteev, A.M. Zeitlin and A. Smirnov is supported in part by AMS Simons travel Grant. A. M. Zeitlin is partially supported by Simons Collaboration Grant, Award ID: 578501. Open access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"TaHa"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["530"],"article_processing_charge":"Yes (via OA deal)","file_date_updated":"2021-09-13T11:31:34Z","intvolume":"        27","author":[{"last_name":"Koroteev","full_name":"Koroteev, Peter","first_name":"Peter"},{"id":"151DCEB6-9EC3-11E9-8480-ABECE5697425","last_name":"Pushkar","first_name":"Petr","full_name":"Pushkar, Petr"},{"last_name":"Smirnov","first_name":"Andrey V.","full_name":"Smirnov, Andrey V."},{"first_name":"Anton M.","full_name":"Zeitlin, Anton M.","last_name":"Zeitlin"}],"oa":1,"_id":"9998","date_published":"2021-08-30T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1007/s00029-021-00698-3","publisher":"Springer Nature","year":"2021","type":"journal_article"},{"_id":"7940","oa":1,"author":[{"last_name":"Yang","id":"360D8648-F248-11E8-B48F-1D18A9856A87","full_name":"Yang, Yaping","first_name":"Yaping"},{"last_name":"Zhao","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","full_name":"Zhao, Gufang","first_name":"Gufang"}],"date_published":"2020-12-01T00:00:00Z","year":"2020","publisher":"Springer Nature","doi":"10.1007/s00031-020-09572-6","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"eissn":["1531586X"],"issn":["10834362"]},"quality_controlled":"1","month":"12","article_type":"original","volume":25,"isi":1,"department":[{"_id":"TaHa"}],"acknowledgement":"Gufang Zhao is affiliated to IST Austria, Hausel group until July of 2018. Supported by the Advanced Grant Arithmetic and Physics of Higgs moduli spaces No. 320593 of the European Research Council.","date_created":"2020-06-07T22:00:55Z","intvolume":"        25","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"lang":"eng","text":"We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay, Regelskis, and Wendlandt [GRW18]."}],"ec_funded":1,"day":"01","oa_version":"Preprint","publication_status":"published","page":"1371-1385","date_updated":"2023-08-21T07:06:21Z","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.04375"}],"title":"The PBW theorem for affine Yangians","external_id":{"arxiv":["1804.04375"],"isi":["000534874300003"]},"publication":"Transformation Groups","citation":{"ieee":"Y. Yang and G. Zhao, “The PBW theorem for affine Yangians,” <i>Transformation Groups</i>, vol. 25. Springer Nature, pp. 1371–1385, 2020.","chicago":"Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” <i>Transformation Groups</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00031-020-09572-6\">https://doi.org/10.1007/s00031-020-09572-6</a>.","ama":"Yang Y, Zhao G. The PBW theorem for affine Yangians. <i>Transformation Groups</i>. 2020;25:1371-1385. doi:<a href=\"https://doi.org/10.1007/s00031-020-09572-6\">10.1007/s00031-020-09572-6</a>","ista":"Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation Groups. 25, 1371–1385.","mla":"Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” <i>Transformation Groups</i>, vol. 25, Springer Nature, 2020, pp. 1371–85, doi:<a href=\"https://doi.org/10.1007/s00031-020-09572-6\">10.1007/s00031-020-09572-6</a>.","short":"Y. Yang, G. Zhao, Transformation Groups 25 (2020) 1371–1385.","apa":"Yang, Y., &#38; Zhao, G. (2020). The PBW theorem for affine Yangians. <i>Transformation Groups</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00031-020-09572-6\">https://doi.org/10.1007/s00031-020-09572-6</a>"},"arxiv":1,"project":[{"name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"320593"}],"scopus_import":"1"},{"date_updated":"2023-08-22T09:00:03Z","status":"public","abstract":[{"text":"Let 𝐹:ℤ2→ℤ be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes. ","lang":"eng"}],"ec_funded":1,"day":"01","page":"1649-1675","publication_status":"published","oa_version":"Preprint","arxiv":1,"citation":{"ama":"Kalinin N, Shkolnikov M. Sandpile solitons via smoothing of superharmonic functions. <i>Communications in Mathematical Physics</i>. 2020;378(9):1649-1675. doi:<a href=\"https://doi.org/10.1007/s00220-020-03828-8\">10.1007/s00220-020-03828-8</a>","apa":"Kalinin, N., &#38; Shkolnikov, M. (2020). Sandpile solitons via smoothing of superharmonic functions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-020-03828-8\">https://doi.org/10.1007/s00220-020-03828-8</a>","short":"N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020) 1649–1675.","ista":"Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 378(9), 1649–1675.","mla":"Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:<a href=\"https://doi.org/10.1007/s00220-020-03828-8\">10.1007/s00220-020-03828-8</a>.","ieee":"N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic functions,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9. Springer Nature, pp. 1649–1675, 2020.","chicago":"Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-020-03828-8\">https://doi.org/10.1007/s00220-020-03828-8</a>."},"project":[{"grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"scopus_import":"1","issue":"9","main_file_link":[{"url":"https://arxiv.org/abs/1711.04285","open_access":"1"}],"title":"Sandpile solitons via smoothing of superharmonic functions","external_id":{"isi":["000560620600001"],"arxiv":["1711.04285"]},"publication":"Communications in Mathematical Physics","year":"2020","publisher":"Springer Nature","doi":"10.1007/s00220-020-03828-8","language":[{"iso":"eng"}],"type":"journal_article","_id":"8325","oa":1,"author":[{"last_name":"Kalinin","full_name":"Kalinin, Nikita","first_name":"Nikita"},{"first_name":"Mikhail","full_name":"Shkolnikov, Mikhail","last_name":"Shkolnikov","id":"35084A62-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4310-178X"}],"date_published":"2020-09-01T00:00:00Z","department":[{"_id":"TaHa"}],"acknowledgement":"We thank Andrea Sportiello for sharing his insights on perturbative regimes of the Abelian sandpile model which was the starting point of our work. We also thank Grigory Mikhalkin, who encouraged us to approach this problem. We thank an anonymous referee. Also we thank Misha Khristoforov and Sergey Lanzat who participated on the initial state of this project, when we had nothing except the computer simulation and pictures. We thank Mikhail Raskin for providing us the code on Golly for faster simulations. Ilia Zharkov, Ilia Itenberg, Kristin Shaw, Max Karev, Lionel Levine, Ernesto Lupercio, Pavol Ševera, Yulieth Prieto, Michael Polyak, Danila Cherkashin asked us a lot of questions and listened to us; not all of their questions found answers here, but we are going to treat them in subsequent papers.","date_created":"2020-08-30T22:01:13Z","intvolume":"       378","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","publication_identifier":{"issn":["00103616"],"eissn":["14320916"]},"quality_controlled":"1","month":"09","article_type":"original","volume":378,"isi":1}]