Alexander Braverman

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 has to do with representation theory of p-adic groups (in particular, p-adic interpretation of Lusztig's asymptotic Hecke algebra and its generalizations).

Recent Publications

• Braverman, Alexander; Finkelberg, Michael; Nakajima, Hiraku Instanton moduli spaces and W-algebras. Astérisque No. 385 (2016),
• arXiv:1807.09038 Coulomb branches of 3-dimensional gauge theories and related structures. Alexander Braverman, Michael Finkelberg.
• arXiv:1805.11826 Line bundles over Coulomb branches. Alexander Braverman, Michael Finkelberg, Hiraku Nakajima.
• arXiv:1804.00336 Schwartz space of parabolic basic affine space and asymptotic Hecke algebras. Alexander Braverman, David Kazhdan.
• arXiv:1706.02112 Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan). Alexander Braverman, Michael Finkelberg, Hiraku Nakajima.
• arXiv:1611.10216 Cyclotomic double affine Hecke algebras (with an appendix by Hiraku Nakajima and Daisuke Yamakawa). Alexander Braverman, Pavel Etingof, Michael Finkelberg.
• arXiv:1604.03625 Coulomb branches of $3d$ $\mathcal N=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes). Alexander Braverman, Michael Finkelberg, Hiraku Nakajima.

Seminars

• Lectures on "Coulomb branches and related mathematical structures" at CIME summer school, Cetraro, June 2018
• UC Davis mathematics colloquium, March 2018
• The 21st Midrasha in Mathematicae: Lie Theory without Groups: Enumerative Geometry and Quantization of Symplectic Resolutions, Institute for Advanced Studies, Hebrew University of Jerusalem, two lectures
• BIRS workshop " Automorphic Forms, Mock Modular Forms and String Theory" invited lecture
• Conference on representation theory and Algebraic Geometry In honor of Joseph Bernstein, Weizmann Institute, June 2017, http://www.weizmann.ac.il/conferences/RTAG2017/
• Representation Theory at the Crossroads of Modern Mathematics (in honor of Alexandre Kirillov). Reims, May 29 - June 2, 2017 http://reims.math.cnrs.fr/pevzner/aak81.html
• String-Math seminar at University of California, Berkeley, https://math.berkeley.edu/~smirnov/MathPhysSeminar/SemArch/StringMathSpring2017.html
• Workshop on Hall Algebras, Enumerative Invariants and Gauge Theories November 14 - 18, 2016, The Fields Institute, http://www.fields.utoronto.ca/activities/16-17/hall-algebras
• Clay worskhop on geometric representation theory, Oxford University, September 2016