[{"ec_funded":1,"file_date_updated":"2021-05-03T06:54:06Z","year":"2021","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.","publisher":"Mathematical Sciences Publishers","department":[{"_id":"TaHa"}],"publication_status":"published","author":[{"full_name":"Ho, Quoc P","first_name":"Quoc P","last_name":"Ho","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87"}],"volume":25,"date_updated":"2023-08-08T13:28:59Z","date_created":"2021-05-02T06:59:33Z","publication_identifier":{"issn":["1364-0380"]},"month":"04","oa":1,"external_id":{"arxiv":["1802.07948"],"isi":["000682738600005"]},"project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","grant_number":"320593","call_identifier":"FP7","name":"Arithmetic and physics of Higgs moduli spaces"},{"_id":"26B96266-B435-11E9-9278-68D0E5697425","grant_number":"M02751","name":"Algebro-Geometric Applications of Factorization Homology","call_identifier":"FWF"}],"isi":1,"quality_controlled":"1","doi":"10.2140/gt.2021.25.813","language":[{"iso":"eng"}],"type":"journal_article","issue":"2","abstract":[{"lang":"eng","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"}],"_id":"9359","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 25","ddc":["514","516","512"],"status":"public","title":"Homological stability and densities of generalized configuration spaces","file":[{"relation":"main_file","file_id":"9366","date_updated":"2021-05-03T06:54:06Z","date_created":"2021-05-03T06:54:06Z","checksum":"643a8d2d6f06f0888dcd7503f55d0920","success":1,"file_name":"densities.pdf","access_level":"open_access","content_type":"application/pdf","file_size":479268,"creator":"qho"}],"oa_version":"Submitted Version","keyword":["Generalized configuration spaces","homological stability","homological densities","chiral algebras","chiral homology","factorization algebras","Koszul duality","Ran space"],"article_processing_charge":"No","has_accepted_license":"1","day":"27","citation":{"chicago":"Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” Geometry & Topology. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/gt.2021.25.813.","mla":"Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” Geometry & Topology, vol. 25, no. 2, Mathematical Sciences Publishers, 2021, pp. 813–912, doi:10.2140/gt.2021.25.813.","short":"Q.P. Ho, Geometry & Topology 25 (2021) 813–912.","ista":"Ho QP. 2021. Homological stability and densities of generalized configuration spaces. Geometry & Topology. 25(2), 813–912.","apa":"Ho, Q. P. (2021). Homological stability and densities of generalized configuration spaces. Geometry & Topology. Mathematical Sciences Publishers. https://doi.org/10.2140/gt.2021.25.813","ieee":"Q. P. Ho, “Homological stability and densities of generalized configuration spaces,” Geometry & Topology, vol. 25, no. 2. Mathematical Sciences Publishers, pp. 813–912, 2021.","ama":"Ho QP. Homological stability and densities of generalized configuration spaces. Geometry & Topology. 2021;25(2):813-912. doi:10.2140/gt.2021.25.813"},"publication":"Geometry & Topology","page":"813-912","article_type":"original","date_published":"2021-04-27T00:00:00Z"},{"file_date_updated":"2021-09-13T11:31:34Z","article_number":"87","date_updated":"2023-08-14T06:34:14Z","date_created":"2021-09-12T22:01:22Z","volume":27,"author":[{"first_name":"Peter","last_name":"Koroteev","full_name":"Koroteev, Peter"},{"id":"151DCEB6-9EC3-11E9-8480-ABECE5697425","last_name":"Pushkar","first_name":"Petr","full_name":"Pushkar, Petr"},{"full_name":"Smirnov, Andrey V.","last_name":"Smirnov","first_name":"Andrey V."},{"full_name":"Zeitlin, Anton M.","first_name":"Anton M.","last_name":"Zeitlin"}],"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"TaHa"}],"year":"2021","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).","month":"08","publication_identifier":{"eissn":["1420-9020"],"issn":["1022-1824"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00029-021-00698-3","quality_controlled":"1","isi":1,"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"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":["000692795200001"]},"oa":1,"abstract":[{"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.","lang":"eng"}],"issue":"5","type":"journal_article","file":[{"relation":"main_file","file_id":"10010","checksum":"beadc5a722ffb48190e1e63ee2dbfee5","success":1,"date_created":"2021-09-13T11:31:34Z","date_updated":"2021-09-13T11:31:34Z","access_level":"open_access","file_name":"2021_SelectaMath_Koroteev.pdf","content_type":"application/pdf","file_size":584648,"creator":"cchlebak"}],"oa_version":"Published Version","status":"public","ddc":["530"],"title":"Quantum K-theory of quiver varieties and many-body systems","intvolume":" 27","_id":"9998","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"30","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","date_published":"2021-08-30T00:00:00Z","article_type":"original","publication":"Selecta Mathematica","citation":{"apa":"Koroteev, P., Pushkar, P., Smirnov, A. V., & Zeitlin, A. M. (2021). Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. Springer Nature. https://doi.org/10.1007/s00029-021-00698-3","ieee":"P. Koroteev, P. Pushkar, A. V. Smirnov, and A. M. Zeitlin, “Quantum K-theory of quiver varieties and many-body systems,” Selecta Mathematica, vol. 27, no. 5. Springer Nature, 2021.","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.","ama":"Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 2021;27(5). doi:10.1007/s00029-021-00698-3","chicago":"Koroteev, Peter, Petr Pushkar, Andrey V. Smirnov, and Anton M. Zeitlin. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” Selecta Mathematica. Springer Nature, 2021. https://doi.org/10.1007/s00029-021-00698-3.","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.” Selecta Mathematica, vol. 27, no. 5, 87, Springer Nature, 2021, doi:10.1007/s00029-021-00698-3."}},{"file_date_updated":"2021-09-21T15:58:52Z","article_number":"107992","volume":392,"date_created":"2021-09-21T15:58:59Z","date_updated":"2023-08-14T06:54:35Z","author":[{"full_name":"Ho, Quoc P","orcid":"0000-0001-6889-1418","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","last_name":"Ho","first_name":"Quoc P"}],"department":[{"_id":"TaHa"}],"publisher":"Elsevier","publication_status":"published","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.","year":"2021","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"month":"09","language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2021.107992","project":[{"_id":"26B96266-B435-11E9-9278-68D0E5697425","grant_number":"M02751","call_identifier":"FWF","name":"Algebro-Geometric Applications of Factorization Homology"}],"quality_controlled":"1","isi":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":["1610.00212"],"isi":["000707040300031"]},"oa":1,"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"}],"type":"journal_article","oa_version":"Published Version","file":[{"file_name":"1-s2.0-S000187082100431X-main.pdf","access_level":"open_access","file_size":840635,"content_type":"application/pdf","creator":"qho","relation":"main_file","file_id":"10034","date_created":"2021-09-21T15:58:52Z","date_updated":"2021-09-21T15:58:52Z","checksum":"f3c0086d41af11db31c00014efb38072"}],"intvolume":" 392","status":"public","ddc":["514"],"title":"The Atiyah-Bott formula and connectivity in chiral Koszul duality","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10033","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"21","keyword":["Chiral algebras","Chiral homology","Factorization algebras","Koszul duality","Ran space"],"scopus_import":"1","date_published":"2021-09-21T00:00:00Z","article_type":"original","citation":{"apa":"Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107992","ieee":"Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” Advances in Mathematics, vol. 392. Elsevier, 2021.","ista":"Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992.","ama":"Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 2021;392. doi:10.1016/j.aim.2021.107992","chicago":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107992.","short":"Q.P. Ho, Advances in Mathematics 392 (2021).","mla":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” Advances in Mathematics, vol. 392, 107992, Elsevier, 2021, doi:10.1016/j.aim.2021.107992."},"publication":"Advances in Mathematics"},{"year":"2020","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"TaHa"}],"author":[{"full_name":"Rapcak, Miroslav","first_name":"Miroslav","last_name":"Rapcak"},{"full_name":"Soibelman, Yan","last_name":"Soibelman","first_name":"Yan"},{"full_name":"Yang, Yaping","first_name":"Yaping","last_name":"Yang"},{"full_name":"Zhao, Gufang","first_name":"Gufang","last_name":"Zhao","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2019-11-12T14:01:27Z","date_updated":"2023-08-17T14:02:59Z","volume":376,"ec_funded":1,"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1810.10402"}],"external_id":{"isi":["000536255500004"],"arxiv":["1810.10402"]},"isi":1,"quality_controlled":"1","project":[{"grant_number":"320593","_id":"25E549F4-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Arithmetic and physics of Higgs moduli spaces"}],"doi":"10.1007/s00220-019-03575-5","language":[{"iso":"eng"}],"month":"06","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7004","title":"Cohomological Hall algebras, vertex algebras and instantons","status":"public","intvolume":" 376","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds.","lang":"eng"}],"publication":"Communications in Mathematical Physics","citation":{"chicago":"Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03575-5.","short":"M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical Physics 376 (2020) 1803–1873.","mla":"Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical Physics, vol. 376, Springer Nature, 2020, pp. 1803–73, doi:10.1007/s00220-019-03575-5.","ieee":"M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras, vertex algebras and instantons,” Communications in Mathematical Physics, vol. 376. Springer Nature, pp. 1803–1873, 2020.","apa":"Rapcak, M., Soibelman, Y., Yang, Y., & Zhao, G. (2020). Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03575-5","ista":"Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873.","ama":"Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 2020;376:1803-1873. doi:10.1007/s00220-019-03575-5"},"article_type":"original","page":"1803-1873","date_published":"2020-06-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No"},{"year":"2020","publication_status":"published","department":[{"_id":"TaHa"}],"publisher":"Springer Nature","author":[{"last_name":"Minets","first_name":"Sasha","orcid":"0000-0003-3883-1806","id":"3E7C5304-F248-11E8-B48F-1D18A9856A87","full_name":"Minets, Sasha"}],"date_created":"2020-04-26T22:00:44Z","date_updated":"2023-08-21T06:14:58Z","volume":26,"article_number":"30","file_date_updated":"2020-07-14T12:48:02Z","external_id":{"isi":["000526036400001"],"arxiv":["1801.01429"]},"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,"quality_controlled":"1","isi":1,"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"doi":"10.1007/s00029-020-00553-x","language":[{"iso":"eng"}],"month":"04","publication_identifier":{"issn":["10221824"],"eissn":["14209020"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7683","title":"Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces","ddc":["510"],"status":"public","intvolume":" 26","file":[{"file_id":"7690","relation":"main_file","checksum":"2368c4662629b4759295eb365323b2ad","date_updated":"2020-07-14T12:48:02Z","date_created":"2020-04-28T10:57:58Z","access_level":"open_access","file_name":"2020_SelectaMathematica_Minets.pdf","creator":"dernst","content_type":"application/pdf","file_size":792469}],"oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"For any free oriented Borel–Moore homology theory A, we construct an associative product on the A-theory of the stack of Higgs torsion sheaves over a projective curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel–Moore homology groups. We also introduce moduli spaces of stable triples, heavily inspired by Nakajima quiver varieties, whose A-theory admits an AHa0C-action. These triples can be interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action of AHa0C on the cohomology of Hilbert schemes of points on T∗C."}],"issue":"2","publication":"Selecta Mathematica, New Series","citation":{"short":"S. Minets, Selecta Mathematica, New Series 26 (2020).","mla":"Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series, vol. 26, no. 2, 30, Springer Nature, 2020, doi:10.1007/s00029-020-00553-x.","chicago":"Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series. Springer Nature, 2020. https://doi.org/10.1007/s00029-020-00553-x.","ama":"Minets S. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 2020;26(2). doi:10.1007/s00029-020-00553-x","ieee":"S. Minets, “Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces,” Selecta Mathematica, New Series, vol. 26, no. 2. Springer Nature, 2020.","apa":"Minets, S. (2020). Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. Springer Nature. https://doi.org/10.1007/s00029-020-00553-x","ista":"Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2), 30."},"article_type":"original","date_published":"2020-04-15T00:00:00Z","scopus_import":"1","day":"15","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1"}]