Alexander Braverman

Alexander Braverman profile picture
University of Toronto
Research Associate Faculty
Areas of research:
Mathematical Physics
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.
  • Full Professor, Brown University, 2009-2015
  • Associate Professor, Brown University, 2004-2009
  • 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
  • Braverman, A., Kazhdan, D., & Polishchuk, A. (2024). Schwartz $?$-densities for the moduli stack of rank $2$ bundles on a curve over a local field. arxiv: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. arxiv:2312.07138v1
  • Braverman, A., Kazhdan, D., & Polishchuk, A. (2023). Hecke operators for curves over non-archimedean local fields and related finite rings. arxiv:2305.09595v2
  • Braverman, A., Kazhdan, D., & Polishchuk, A. (2023). Automorphic functions for nilpotent extensions of curves over finite fields. arxiv:2303.16259v1
  • Bezrukavnikov, R., Braverman, A., Finkelberg, M., & Kazhdan, D. (2023). A fusion construction of local L-factors. doi:10.48550/arxiv.2303.00913
  • Braverman, A., Finkelberg, M., & Nakajima, H. (2022). Kazhdan–Lusztig conjecture via zastava spaces. Journal für die reine und angewandte Mathematik (Crelles Journal), 2022(787), 45-78. doi:10.1515/crelle-2022-0013
  • Braverman, A., Dhillon, G., Finkelberg, M., Raskin, S., & Travkin, R. (2022). Coulomb branches of noncotangent type (with appendices by Gurbir Dhillon and Theo Johnson-Freyd). doi:10.48550/arxiv.2201.09475
  • Bezrukavnikov, R., Braverman, A., & Mirkovic, I. (2022). Corrigendum to “Some results about geometric Whittaker model” [Adv. Math. 186 (1) (2004) 143–152]. Advances in Mathematics, 394, 108014. doi:10.1016/j.aim.2021.108014
  • Braverman, A., Finkelberg, M., & Travkin, R. (2022). Orthosymplectic Satake equivalence. Communications in Number Theory and Physics, 16(4), 695-732. doi:10.4310/cntp.2022.v16.n4.a2
  • Braverman, A., & Finkelberg, M. (2022). A Quasi-Coherent Description of the Category D -mod(GrGL(n)). In Representation Theory and Algebraic Geometry (pp. 133-149). Springer Nature. doi:10.1007/978-3-030-82007-7_5
  • Braverman, A., & Kazhdan, D. (2021). Automorphic functions on moduli spaces of bundles on curves over local fields: a survey. arxiv:2112.08139v2
  • Braverman, A., Finkelberg, M., Ginzburg, V., & Travkin, R. (2021). Mirabolic Satake equivalence and supergroups. Compositio Mathematica, 157(8), 1724-1765. doi:10.1112/s0010437x21007387
  • Braverman, A., Finkelberg, M., & Travkin, R. (2021). Gaiotto conjecture for $Rep_q(GL(N-1|N))$. doi:10.48550/arxiv.2107.02653
  • Braverman, A., Finkelberg, M., & Nakajima, H. (2021). Line bundles over Coulomb branches. Advances in Theoretical and Mathematical Physics, 25(4), 957-993. doi:10.4310/atmp.2021.v25.n4.a2
  • 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
  • Mini course on symplectic duality, SwissMAP winter school on mathematical physics, 2023/01/09
  • Hecke operators on moduli spaces on bundles over local fields, Algebraic Geometry, Mathematical Physics, and Solitons, Columbia University, Mathematics, New York, United States, 2022/10/09
  • : S-duality for boundary conditions coming from Lie super-algebras, Geometric Representation Theory, Integrability, and Supersymmetric Gauge Theories, Stony Brook University, Simons Center for Geometry and Physics, Stony Brook, United States, 2022/09/28
  • Derived geometric Satake equivalence and geometric construction of S-duality for boundary conditions, Gauged Maps, Vortices and Their Moduli, SwissMap, 2022/08/24
  • Discussion on Langlands, QFT for Mathematicians 2022, 2022/06/30, PIRSA:22060094
  • Lie superalgebras and S-duality, QFT for Mathematicians 2022, 2022/06/30, PIRSA:22060093
  • Coulomb branches of non-cotangent type, Vertex algebras and Poisson geometry, Les Diablerets, Switzerland, 2022/01/01
  • S-duality and super-algebras, Geometric representation theory, ICM 2022 sattelite conference, IPMU, Tokyo, 2022/01/01