# Alexander Braverman

University of Toronto

Areas of research:

### Research Interests

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.

### Recent Publications

- Orthosymplectic Satake equivalence, Alexander Braverman, Michael Finkelberg, Roman Travkin, arXiv: 1912.01930, to appear in Communications in Number Theory and Physics
- Kazhdan-Lusztig conjecture via zastava spaces. Braverman, Alexander; Finkelberg, Michael; Nakajima, Hiraku, J. Reine Angew. Math. 787 (2022), 45-78.
- Line bundles on Coulomb branches. Braverman, Alexander; Finkelberg, Michael; Nakajima, Hiraku, Adv. Theor. Math. Phys. 25 (2021), no. 4, 957-993.
- Orthosymplectic Satake equivalence, II, Alexander Braverman, Michael Finkelberg, Roman Travkin, arXiv: 2207.03115
- Coulomb branches of noncotangent type (with appendices by Gurbir Dhillon and Theo Johnson-Freyd), Alexander Braverman, Gurbir Dhillon, Michael Finkelberg, Sam Raskin, Roman Travkin,
- Automorphic functions on moduli spaces of bundles on curves over local fields: a survey, Alexander Braverman, David Kazhdan, arXiv: 2112.08139
- 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

### Seminars

- Invited talk at "Geometric representation theory", ICM 2022 sattelite conference (hosted online by IPMU, Tokyo), "S-duality and super-algebras"
- "Coulomb branches of non-cotangent type". Invited talk at the wokrshop "Vertex algebras and Poisson geometry", Les Diablerets, Switzerland
- "Coulomb branches of non-cotangent type". Boston University geometry and physics seminar
- "Hecke eigen-functions for curves over local non-archimedian fields", MIT Lie groups seminar
- "One ring to rule them all". Representation theory workshop in MFO, Oberwolfach, Germany
- Hecke eigen-functions for curves over local non-archimedian fields", Yale representation theory seminar