University of Toronto - Department of Mathematics
Areas of research: Mathematical Physics
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.
Positions Held
- Full Professor, Brown University, 2009-2015
- Associate Professor, Brown University, 2004-2009
Awards
- Frontiers of Science Award, The International Congress for Basic Science, 2023
- Frontiers of Science Award, International Congress of Basic Science, 2023
- Discovery Grant, Natural Sciences and Engineering Research Council of Canada (NSERC), 2022-2027
Recent Publications
- Braverman, A., Dhillon, G., Finkelberg, M., Raskin, S., & Travkin, R. (2025). Coulomb branches of noncotangent type (with appendices by Gurbir Dhillon and Theo Johnson-Freyd). doi:10.48550/arxiv.2201.09475
- Braverman, A., Kazhdan, D., Polishchuk, A., & Wong, K. F. (2025). Hecke Operators for Curves Over Non-Archimedean Local Fields and Related Finite Rings. International Mathematics Research Notices, 2025(7), rnaf075. doi:10.1093/imrn/rnaf075
- Braverman, A., Finkelberg, M., Kazhdan, D., & Travkin, R. (2024). Relative Langlands duality for $\mathfrak{osp}(2n + 1|2n)$. doi:10.48550/arxiv.2412.20544
- Braverman, A., Finkelberg, M., & Travkin, R. (2024). Gaiotto conjecture for $\operatorname{Rep}_q(\operatorname{GL}(N-1 \mid N))$. Pure and Applied Mathematics Quarterly, 21(2), 663-695. doi:10.4310/pamq.241205003652
- Braverman, A., Kazhdan, D., & Polishchuk, A. (2024). Schwartz $?$-densities for the moduli stack of rank $2$ bundles on a curve over a local field. https://arxiv.org/abs/2401.01037v2
- Braverman, A., & Kazhdan, D. (2023). Hecke algebras for the 1st congruence subgroup and bundles on ${\mathbb P}^1$ I: the case of finite field. https://arxiv.org/abs/2312.07138v1
- Braverman, A., Kazhdan, D., Polishchuk, A., & Wong, K. F. (2023). Hecke operators for curves over non-archimedean local fields and related finite rings. https://arxiv.org/abs/2305.09595v4
- Braverman, A., Kazhdan, D., & Polishchuk, A. (2023). Automorphic functions for nilpotent extensions of curves over finite fields. https://arxiv.org/abs/2303.16259v1
- Bezrukavnikov, R., Braverman, A., Finkelberg, M., & Kazhdan, D. (2023). A fusion construction of local L-factors. doi:10.48550/arxiv.2303.00913
Seminars
- Koszul duality in Relative Langlands duality/S-duality, Simons Center for Geometry and Physics, 2025/04/03
- Koszul duality for some categories of D-modules coming from relative Langlands duality and equivariant localization for equivariant D-module categories, University of Montreal, CRM, Montreal, QC, Canada, 2024/09/19
- S-duality and Lie super-algebras, BIMSA, China, 2024/07/19
- Hecke eigen-functions for curves over local non-archimedian fields, Max Planck Institute for Mathematics, Bonn, Germany, 2024/04/23
- Hecke operators for algebraic curves over local non-archimedian fields: a survey of some recent results, Harvard University, CMSA, Cambridge, United States, 2024/03/26
- Calogero-Moser spaces and Hecke operators, 2024/01/31
- Hecke operators over local fields, Calogero-Moser varieties and lifting, MIT, Mathematics, 2023/11/03
- Gaiotto conjectures from geometric Langlands point of view, Gauge Theory, Moduli Spaces and Representation Theory, Kyoto University, Mathematics, Kyoto, Japan, 2023/02/22