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 has to do with representation theory of p-adic groups (in particular, p-adic interpretation of Lusztig's asymptotic Hecke algebra and its generalizations).
- arXiv: 2007.09799 Kazhdan-Lusztig conjecture via Zastava spaces, Alexander Braverman, Michael Finkelberg, Hiraku Nakajima
- arXiv: 1912.01930 Orthosymplectic Satake equivalence, Alexander Braverman, Michael Finkelberg, Roman Travkin https://arxiv.org/abs/1912.01930
- arXiv: 1909.11492 Mirabolic Satake equivalence and supergroups, Alexander Braverman, Michael Finkelberg, Victor Ginzburg, Roman Travkin https://arxiv.org/abs/1909.11492
- 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
- 3d gauge theories and local geometric Langlands, "Geometric Langlands office hours" (Harvard), 2 talks
- Kazhdan-Lusztig conjecture via Zastava spaces, Vienna representation theory seminar (online)
- 1 hour talk at The 10th Conference of Tsinghua Sanya Internationl Mathematics Forum--Geometric Representation Theory and Quantum Field Theories