Homepage of Mikhail Gorsky
I am a postdoc at the Department of Mathematics at the University of Hamburg.
In 2022-2024, I was a postdoc at the University of Vienna. In 2021-2022, I was a postdoc at LAMFA at the Université de Picardie Jules Verne in Amiens. I spent the 2020 fall semester at the Hausdorff Research Institute for Mathematics in Bonn. In 2018-2020, I was a postdoc at the University of Stuttgart. Prior to that I was a visiting scientist at the Bielefeld University and an invited reseascher at IHES. In 2015-2017, I was a postdoctoral fellow at the Max Planck Institute of Mathematics in Bonn.
Contacts
E-mail: mikhail.gorskii at univie.ac.at; mikhail.gorskii at uni-hamburg.de
(The current official transliteration of my last name is "Gorskii")
Organising
In January 2022, Roger Casals, José Simental Rodríguez, Melissa Sherman-Bennett and I organised AIM workshop on cluster algebras and braid varieties.
In July 2021 -- December 2022, José Simental Rodríguez and I ran an online seminar on cluster structures on coordinate rings of various varieties appearing in Lie theory and related to link invariants. It was organised within the AIM Research Community on Link Homology.
Research interests
Hall algebras and categorification of quantum groups
Cluster algebras and cluster categories
Quiver representations and quiver varieties
Coxeter combinatorics: subword complexes, Cambrian lattices, non-crossing partitions...
Categorification of knot invariants
Publications
(with Roger Casals, Eugene Gorsky, Ian Le, Linhui Shen, and José Simental) Cluster structures on braid varieties. Journal of the American Mathemathical Society 38, no. 2 (2025): 369--479. https://doi.org/10.1090/jams/1048 arXiv:2207.11607
(with Roger Casals, Eugene Gorsky, and José Simental) Algebraic weaves and braid varieties. American Journal of Mathematics 146, no. 6 (2024): 1469--1576. https://dx.doi.org/10.1353/ajm.2024.a944357 . arXiv:2012.06931
(with Teresa Conde, Frederik Marks, and Alexandra Zvonareva) A functorial approach to rank functions on triangulated categories. Journal für die reine und angewandte Mathematik (Crelle's Journal) , vol. 2024, no. 811, 2024, pp. 135-181, doi 10.1515/ crelle-2024-0009 arXiv:2209.00898
(with Rose-Line Baillargeon, Thomas Brüstle, and Souheila Hassoun) On the lattices of exact and weakly exact structures. Journal of Algebra, Volume 612, December 2022, pp 77--109. arXiv:2009.10024
(with Xin Fang) Exact structures and degeneration of Hall algebras. Advances in Mathematics, Volume 398, March 2022, 108210. arXiv:2005.12130
Semi-derived and derived Hall algebras for stable categories. International Mathematics Research Notices, 2018, Vol. 2018, Issue 1, pp 138--159. arXiv:1409.6798
Subword complexes and edge subdivisions. Proceedings of the Steklov Institute of Mathematics, 2014, Vol. 286, pp. 114–127. arXiv:1305.5499
Subword complexes and 2-truncated cubes. Russian Math. Surveys 69 (2014) no. 3. arXiv:2011.05078
Subword complexes and nil-Hecke moves. Modelling and analysis of information systems 20 (2013) no. 6. arXiv:1311.3948
Proof of Gal's conjecture for the D series of generalized associahedra. Russian Math. Surveys 65 (2010) no.6. arXiv:1106.1840
Expository
(with José Simental) Clusters and weaves. (An invited expository article in the Notices of AMS). A different version of this note, with a different title, is available on the arXiv: "Cluster algebras in Lie and knot theory", arXiv:2308.12935
Curious Lefschetz property. PDF (Oberwolfach Report for Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture).
Cluster algebras and symplectic topology: Microlocal holonomies and the Bott-Samelson case. PDF (Oberwolfach Report for Arbeitsgemeinschaft: Cluster Algebras).
Preprints
(with Fabian Haiden) Counting in Calabi--Yau categories, with applications to Hall algebras and knot polynomials. arXiv:2409.10154
(with Marco Castronovo, José Simental, and David E Speyer) Cluster deep loci and mirror symmetry. arXiv:2402.16970
(with Xin Fang, Yann Palu, Pierre-Guy Plamondon, and Matthew Pressland) Extriangulated ideal quotients, with applications to cluster theory and gentle algebras. arXiv:2308.05524
(with Hiroyuki Nakaoka and Yann Palu) Hereditary extriangulated categories: silting objects, mutation, negative extensions. arXiv:2303.07134
(with Nicholas Williams) A structural view of maximal green sequences. arXiv:2301.08681
(with Roger Casals, Eugene Gorsky, and José Simental) Positroid links and braid varieties. arXiv:2105.13948
(with Hiroyuki Nakaoka and Yann Palu) Positive and negative extensions in extriangulated categories. arXiv:2103.12482
Semi-derived Hall algebras and tilting invariance of Bridgeland-Hall algebras. arXiv:1303.5879
(with Eugene Gorsky) A braid group action on parking functions. arXiv:1112.0381
On Young diagrams, flips and cluster algebras of type A. arXiv:1106.2458
Theses
Algèbres de Hall et localisation des catégories, Ph. D. thesis (Abstract and Introduction are both in English and in French, the rest is in English). Université de Paris. Defended in 2019. PDF
Geometry and combinatorics of subword complexes and their dual polytopes, Ph. D. thesis (in Russian). Steklov Mathematical Institute. Defended in 2014. Available at http://www.mi.ras.ru/dis/ref14/gorskii/gorskii_dis.pdf
Slides
Below are slightly corrected versions of presentations for some of my talks.
Videos
Weave calculus and braid varieties, Conference "Categorical braid group actions and categorical representation theory", UMass, Amherst.
Hall algebras and localization of categories , Workshop on Hall algebras, Enumerative Invariants and Gauge Theories, Fields Institute.
Semi-derived Hall algebras , Quiver Varieties Workshop, Simons Center for Geometry and Physics.
Geometry and combinatorics of subword complexes and dual polytopes , Conference "Geometry, Topology, and Applications", Yaroslavl State University.
Hall algebras and quantum groups , Simons Center for Geometry and Physics.
Teaching
WS 2024 – 2025: Algebra, Universität Hamburg
SS 2020: Höhere Mathematik 2, Universität Stuttgart
WS 2019 – 2020: Höhere Mathematik 3, Universität Stuttgart.
SS 2019: Algebra 2, Universität Stuttgart.
WS 2018 – 2019: Höhere Mathematik 3, Universität Stuttgart.
2014 – 2016: Responsable de Travaux Dirigés, algèbre et analyse élémentaires, L1 info at Université Paris VII.