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

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

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

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

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

Preprints

1. Stability associahedra, maximal green sequences and second Cambrian orders, in preparation.

2. (with Xin Fang) Extriangulated structures and degeneration of Hall algebras, in preparation.

3. Hall algebras of extriangulated categories, to appear.

4. Hall algebras and localization of categories I, to appear. Preliminary version available upon request.

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

6. (with Roger Casals, Eugene Gorsky, and José Simental) Algebraic weaves and braid varieties. arXiv:2012.06931

7. (with Rose-Line Baillargeon, Thomas Brüstle, and Souheila Hassoun) On the lattices of exact and weakly exact structures. arXiv:2009.10024

8. (with Xin Fang) Exact structures and degeneration of Hall algebras. arXiv:2005.12130

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

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

• 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

• 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 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.