Homepage of Mikhail Gorsky

I am a postdoc at LAMFA at the Université de Picardie Jules Verne in Amiens. My position is supported by the ANR CHARMS. 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.gorsky at iaz.uni-stuttgart.de


Seminars

Since July 2021 José Simental Rodríguez and I are organizing an online seminar on cluster structures on coordinate rings of various varieties appearing in Lie theory and related to link invariants. It is organised as a part of 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

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

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

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

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

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

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

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

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

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

  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

Videos

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.