My main area of research is geometric representation theory (with applications to algebraic geometry, number theory and mathematical physics). Currently I am working on two main subjects: the first (jointly with M.Finkelberg and H.Nakajima) is an attempt to give a mathematically rigorous approach to the study of 3-dimensional N=4 super-symmetric gauge theories and their quantizations and study representations of the resulting non-commutative algebras. The 2nd subject is related to the p-adic version of the recent series of papers by Etingof, Frenkel and Kazhdan. In those paper the authors study eigen-values of certain Hecke operators acting on the space of L2 half-forms on the moduli space of bundles on a curve over real or complex field. In my current work in progress with Kazhdan and Etingof we are trying to develop p-adic analog of that work.
- Alexander Braverman, Michael Finkelberg, Roman Travkin Gaiotto conjecture for Rep_q(GL(Nâ1|N)) arXiv: 2107.02653
- Coulomb branches of 3-dimensional gauge theories and related structures, A.Braverman and M.Finkelberg, in: Geometric Representation Theory and Gauge Theory, C.I.M.E. Foundation Subseries, Editors: Bruzzo, Ugo, Grassi, Antonella, Sala, Francesco (Eds.), https://www.springer.com/gp/book/9783030268558
- Invited talk at String-Math conference
- "Moore-Tachikawa varieties and and their generalizations", invited talk at Shafarevich seminar, Moscow
- Two talks at "Geometric Langlands office hours" seminar at Harvard
- Invited talk at Banff workshop "Geometry, Analysis, and Quantum Physics of Monopoles"
- "Category O via Zastava spaces", invited talk at representation theory seminar, UMass Amherst