Homepage of Mikhail Gorsky

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

1. (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 

2. (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 

3. (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 

4. (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 

5. (with Xin Fang) Exact structures and degeneration of Hall algebras. Advances in Mathematics, Volume 398, March 2022, 108210.  arXiv:2005.12130 

6. Semi-derived and derived Hall algebras for stable categories. International Mathematics Research Notices, 2018, Vol. 2018, Issue 1, pp 138--159.  arXiv:1409.6798 

7. Subword complexes and edge subdivisions. Proceedings of the Steklov Institute of Mathematics, 2014, Vol. 286, pp. 114–127. arXiv:1305.5499

8. Subword complexes and 2-truncated cubes. Russian Math. Surveys 69 (2014) no. 3.  arXiv:2011.05078 

9. Subword complexes and nil-Hecke moves. Modelling and analysis of information systems 20 (2013) no. 6.  arXiv:1311.3948

10. Proof of Gal's conjecture for the D series of generalized associahedra. Russian Math. Surveys 65 (2010) no.6.  arXiv:1106.1840

Expository

1. (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 

2. Curious Lefschetz property. PDF  (Oberwolfach Report for Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture).

3. Cluster algebras and symplectic topology: Microlocal holonomies and the Bott-Samelson case.  PDF  (Oberwolfach Report for Arbeitsgemeinschaft: Cluster Algebras).

Preprints

1. (with Nicholas Williams) Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences. arXiV:2506.08858 

2. (with Fabian Haiden) Counting in Calabi--Yau categories, with applications to Hall algebras and knot polynomials. arXiv:2409.10154 

3. (with Marco Castronovo, José Simental, and David E Speyer) Cluster deep loci and mirror symmetry.  arXiv:2402.16970 

4. (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  

5. (with Hiroyuki Nakaoka and Yann Palu) Hereditary extriangulated categories: silting objects, mutation, negative extensions. arXiv:2303.07134 

6. (with Nicholas Williams) A structural view of maximal green sequences. arXiv:2301.08681 

7. (with Roger Casals, Eugene Gorsky, and José Simental) Positroid links and braid varieties. arXiv:2105.13948 

8. (with Hiroyuki Nakaoka and Yann Palu) Positive and negative extensions in extriangulated categories.  arXiv:2103.12482 

9. Semi-derived Hall algebras and tilting invariance of Bridgeland-Hall algebras. arXiv:1303.5879

10. (with Eugene Gorsky) A braid group action on parking functions. arXiv:1112.0381

11. 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.

• Quivers with potential and Demazure weaves 

• Braid varieties, positroids, and Legendrian links 

•  Algebraic weaves and braid varieties 

• Braid varieties, torus actions and stratifications 

• Exact structures and degeneration of Hall algebras

• Stability associahedra

• Algèbres amassées et algèbres de Hall

• Geometry and Combinatorics of subword complexes and dual polytopes

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

        SS 2025: Lie groups and algebraic groups, Universität Hamburg 

        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.