Bhama Srinivasan

Professor of Mathematics
 

Here are a few quick facts about me. I obtained my Ph.D at the University of Manchester, England under the direction of J.A. (Sandy) Green. I have been at UIC since 1980. My research is in the area of Group theory, specifically in the theory of Representations of finite groups. Like many of my colleagues I have taught courses at all levels in our Department, ranging from Calculus to Representation Theory. (Contrary to what my picture says, I don't teach Shakespeare. However, Shakespeare was PreCalculus, wasn't he?)

ADDRESS

Department of Mathematics, Statistics, and Computer Science (M/C 249)
University of Illinois at Chicago
851 S. Morgan Street
Chicago, IL 60607-7045
e-mail: srinivas@uic.edu
Office Phone: (312) 413-2160
Fax: (312) 996-1491

RESEARCH

My research is in the area of Representation Theory of Finite Groups. Since the structure of an abstract finite group is often difficult to understand, one tries to represent it by a group of matrices over some field. The theory of finite group representations has had a rich history over the last 100 years (see e.g. an article by Charles Curtis in the Math. Intelligencer 14 (1992)). In this century a central figure was Richard Brauer who founded the theory of modular representations of finite groups.
In particular I work with finite reductive groups, which are analogues of Lie groups over finite fields. A big breakthrough in the representation theory of finite reductive groups occurred with the work of George Lusztig in the late 1970's and the 1980's. He introduced tools such as l-adic cohomology and intersection cohomology into the theory, which was then changed for ever. My work since the early 1980's, some of it with my colleague Paul Fong, has been the study of l-modular representations of finite classical groups. Our work has led to further work in this direction in Aachen, Kassel and Paris. An exposition of our work appears in a recent research monograph, "Representations of finite reductive groups" by M.Cabanes and M.Enguehard, Cambridge (2004).
The representation theory of finite classical groups also has rich connections with Combinatorics. Combinatorial objects such as Young tableaux and symmetric functions such as Hall-Littlewood functions arise in a natural way. I am also interested in these symmetric functions.

TEACHING

In Fall 2011 I taught



RECENT PAPERS

Isolated Blocks in finite classical groups, II, J.Algebra 319 (2008), 824-832. Isolated Blocks, II

Modular Representations, old and new , in "Buildings, Geometries and Groups", Springer Proceedings in Mathematics (PROM)(2011) Modular Representations, old and new

Semisimple symplectic characters of finite unitary groups (with C.Ryan Vinroot), J.Algebra 315 (2012), 459-466. (with Ryan Vinroot) Semisimple symplectic characters of finite unitary groups

Quadratic unipotent blocks in general linear, unitary and symplectic groups, J.Group Theory 16 (2013), 825-850. Quadratic unipotent blocks in general linear, unitary and symplectic groups


On CRDAHA and finite general linear and unitary groups, preprint On CRDAHA, and general linear and unitary groups


In preparation :

(with M.Broue, P.Fong) Global-local bijections in finite reductive groups


TALKS Link to a talk at Banff, 2014: BMM_Global Local Bijection in GL(n,q)

Link to a talk at a Satellite Conference to ICM, Bangalore, 2010: Modular Representations, Old and New

Link to a talk at a Satellite Conference to ICM, Bangalore, 2010: Modular Representations, Old and New

Link to a talk at the Newton Institute, June 2009 Quadratic unipotent blocks