Rate My Professor Victor Ginzburg

Victor Ginzburg is a Professor in the Department of Mathematics at the University of Chicago, specializing in geometric representation theory and noncommutative geometry. He earned his PhD in 1985 from Lomonosov Moscow State University, advised by Alexandre Kirillov. Geometric representation theory applies algebraic geometry to study representations of algebras key to representation theory, including classification of irreducible representations of Hecke algebras via K-theory and perverse sheaves in connection with the Deligne-Langlands-Lusztig conjecture; applications of D-modules and perverse sheaves to representations of complex or real reductive groups and semisimple Lie algebras, relating to the Kazhdan-Lusztig conjecture; study of integrable representations of quantum groups using quiver varieties as developed by Nakajima; and contributions to the geometric Langlands program. In noncommutative geometry, Ginzburg's work draws inspiration from quiver theory, which he frequently teaches in a dedicated course, as well as mirror symmetry, Calabi-Yau categories, and mathematical structures from string theory.