Emmy Noether Lectures

1990 Lecturer: Bhama Srinivasan

The Invasion of Geometry into Finite Group Theory
(dedicated to the memory of Louise Hay)

Bhama Srinivasan was born in 1935 in Madras, India. She received her BA and MSc degrees from the University of Madras and went to England for further graduate study. She received her PhD in 1960 under the direction of J. A. Green at the University of Manchester. She taught in England at the University of Keele, held a postdoctoral fellowship at the University of British Columbia, and also taught at the Ramanujan Institute of Mathematics, University of Madras. She came to the United States in 1970 and taught at Clark University until 1979, and since then has been a professor at the University of Illinois at Chicago. She became a U.S. citizen in 1977.
Srinivasan served as President of the Association for Women in Mathematics during 1981-1983. She was a member at the Institute for Advanced Study in 1977 and at the Mathematical Sciences Research Institute in 1990, and has held visiting professorships at the Ecole Normale Superieure in Paris, the University of Essen in the Federal Republic of Germany, Sydney University in Australia, and the Science University of Tokyo in Japan. In January 1979, she presented an AMS Invited Address at the Joint Mathematics Meetings in Biloxi, Mississippi. She served as an editor of the Proceedings of the AMS (1983-1987), Communications in Algebra(1978-1984), andMathematical Surveys and Monographs(1991-1993), and is a member of the Editorial Boards Committee of the AMS (1991-1994).
Srinivasan’s Noether Lecture focused on a topic in her main research area, the representation theory of finite groups. Her talk described how various geometric methods entered group theory and discussed some major results growing out of this approach. The classification in 1981 of finite simple groups revealed that (except for the alternating groups and twenty-six sporadic groups) they are all finite groups of Lie type–that is, groups which are analogs of Lie groups. One problem is classifying the representations of these groups both over the field of complex numbers and over fields of positive characteristic. Since these groups can be regarded as groups of rational points of algebraic groups, techniques from algebraic geometry can be used. Starting with the famous Deligne-Lusztig paper in 1976, such sophisticated geometric tools asl-adic cohomology and intersection cohomology were used, mainly by Lusztig, to classify the complex representations of finite groups of Lie type. Srinivasan’s own work with Paul Fong on the modular representations of these groups benefited from these methods.
“My own view of mathematics through the years has been that ‘truth and beauty are enough’,” she remarks, recalling a  New York Times article about mathematics entitled “Aren’t truth and beauty enough?” “In fact, I have often reminded my students that the best mathematical achievements took place when the question, ‘What is it for?’ was not asked,” she notes. “However, the beautiful interactions with physics which have been going on in recent years have made an impact on me too. The modular representations of finite groups of Lie type have now been linked to quantum groups by the work of Lusztig, and this is very exciting.”