Eugene Gorsky

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Publications and preprints

Teaching

Presentations and talks

Slides and lecture notes

1. Generic curves and non-coprime Catalans ,
   Enumerative geometry of the Hilbert scheme of points, Les Diablerets, February 2024.
2. Jet spaces and link homology ,
   JMM, San Francisco, January 2024.
3. Affine Springer fiber - sheaf correspondence ,
   Gauge Theory, Moduli Spaces and Representation Theory, Kyoto, February 2023.
4. Braid varieties ,
   Yale Colloquium, December 2022.
5. Cluster structures on braid varieties ,
   UCLA Combinatorics Seminar, October 2022.
6. Triply graded link homology: results and structures ,
   Georgia Topology Conference, May 2022.
7. Algebra, geometry and combinatorics of link homology ,
   Colloque des Sciences Mathématiques du Québec, March 2022.
8. The Trace of the affine Hecke category ,
   Recent Developments in Link Homology, SwissMAP Research Station, January 2022.
9. Algebra and geometry of link homology
   IHES 2021 Summer School "Enumerative Geometry, Physics and Representation Theory".
   Lecture 1 notes , video
   Lecture 2 notes , video
   Lecture 3 notes , video
   Lecture 4 notes , video
   Lecture 5 notes , video
   Extended lecture notes arxiv:2108.10356
10. Tautological classes and symmetry in HOMFLY homology ,
    Perspectives on Knot Homology, Banff, May 2021.
11. Tautological classes and symmetry in HOMFLY homology ,
    Topology Seminar, Stanford University, April 2021.
12. Knot invariants and interpolation Macdonald polynomials ,
    Representation Theory seminar, UC Riverside, March 2021.
13. Symmetric functions and link invariants ,
    Colloquium, University of Virginia, February 2021.
14. Braid varieties and algebraic weaves ,
    Representation Theory Oberseminar, Bonn, January 2021.
15. Braids, matrices and character varieties (after Mellit) ,
    Singularity theory seminar, Moscow, October 2020.
16. Parabolic Hilbert schemes on singular curves and representation theory ,
    Representation theory seminar, University of Massachussetts, August 2020.
17. Hilbert schemes of singular curves ,
    Singularity theory seminar, Moscow, May 2020.
18. Derived traces of Soergel categories ,
    GRT at home seminar, Vienna, April 2020.
19. Algebraic geometry and knot invariants ,
    Introductory talk for graduate students, UC Davis, January 2020.
20. Four lectures on Carlsson-Mellit algebra (in Russian).
    Higher School of Economics, Moscow, Russia, December 2018.
21. Hilbert schemes and link homology,
    UC Berkeley colloquium, October 2018.
22. Lectures on Hecke algebras, Soergel bimodules and knot invariants : 1,2,3 (in Russian)
    School on Lie algebras, algebraic groups and invariants, Samara, Russia, August 2018.
23. Dyck path algebra and the Hilbert schemes,
    AMS sectional meeting, Riverside, November 2017.
24. Khovanov-Rozansky homology and the flag Hilbert scheme ,
    Mathematical Congress of the Americas, Montreal, July 2017.
25. Stable bases and q-Fock space,
    Formal Power Series and Algebraic Combinatorics, London, July 2017.
26. Torus knots and rational Catalan combinatorics ,
    Equivariant Combinatorics, CRM, Montreal, June 2017.
27. Knot invariants, Hilbert schemes and Macdonald polynomials ,
    Colloquiums at UPenn and USC, March 2017.
28. Six lectures on Khovanov-Rozansky homology and Hilbert schemes,
    Northeastern University, September 2016.
29. Rational Catalan Combinatorics ,
    Bay Area Discrete Math Day, October 2015.
30. Stable bases and q-Fock space ,
    Representation Theory and Geometry of Symplectic Resolutions, Boston, May 2015.
31. Singular curves and link invariants ,
    Congress of Spanish Royal Mathematical Society, Granada, February 2015.
32. Refined Knot Invariants and Hilbert Schemes
    AGNES, Stony Brook, April 2014.
33. Torus Knots and Rational Cherednik Algebras
    Knots in Washington XXXVII, Washington DC, January 2014.
34. Khovanov Homology and Torus Knots
    Colloquium at Temple University, October 2013.
35. Cherednik algebras, Hilbert schemes and knot invariants.
    AMS Spring Eastern Sectional Meeting. Boston, April 2013
36. On stable Khovanov homology of torus knots
    Knots in Washington XXXV. Washington DC, December 2012.
37. Torus knots and q,t-Catalan numbers
    Simons Postdoctoral Fellows Meeting, Stony Brook, April 2012.
38. Motivic Poincaré series and knot homology
    Second International Workshop on Zeta Functions in Algebra and Geometry , Palma de Mallorca, May 2010.
39. The equivariant Euler characteristic of the moduli spaces of pointed hyperelliptic curves
    Combinatorics of Moduli Spaces, Hurwitz Numbers, And Cluster Algebras. Moscow, June 2008.

Videos

1. Explicit recursion for Khovanov-Rozansky homology (in Russian) ,
   Higher School of Economics, Moscow Russia, December 2019.
2. The full twist category , Categorification in quantum topology and beyond,
   Erwin Schrodinger International Institute for Mathematics and Physics, Vienna, Austria, January 2019.
3. Hilbert schemes and knot homology: lectures 1 , 2 , 3 , 4 .
   Winter school on Categorification, representation theory and symplectic geometry.
   Hausdorff Research Institute for Mathematics, Bonn, Germany, November 2017.
4. On the set of L-space surgeries for links.
   Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, March 2017.
5. Khovanov-Rozansky homology and the flag Hilbert scheme.
   Workshop on Hall Algebras, Enumerative Invariants and Gauge Theories, Fields Institute, November 2016.
6. Homology of Jucys-Murphy elements and the flag Hilbert scheme .
   Quantum Topology, Steklov Math Institute, Moscow, June 2016.
7. Two talks at graduate workshop on geometry of Hilbert schemes:
   Introduction to Hilbert schemes on singular curves ,
   Hilbert schemes of singular curves and Catalan numbers .
   Simons Center for Geometry and Physics, November 2013.
8. Refined knot invariants and Hilbert schemes. Quiver Varieties Program Seminar,
   Simons Center for Geometry and Physics, October 2013.
9. On homological invariants of torus knots. Workshop on Low-dimensional Topology,
   Simons Center for Geometry and Physics, May 2013.
10. Poincaré Series of Algebraic Links and Lattice Homology.
    Topology Seminar, Stony Brook University, February 2013.