Institute for Advanced Study
Election Year: 1992
Primary Section: 11, Mathematics
Membership Type: Member
I am a geometer with a specialization in singularities. Singularities are points where a geometric object is not smooth, i.e., points where the behavior is special as compared to most other points. I have participated in the creation of new techniques for the study of singularities. Examples include intersection homology (joint with M. Goresky), singular characteristic classes (joint with M. Goresky, P. Baum, and W. Fulton), and stratified Morse theory (joint with M. Goresky). Many geometric objects that naturally arise in other areas of mathematics and its applications have singularities. This had led me to do research in these other areas. For example, I have worked in combinatorics (particularly matroid theory and convex polytopes), in modular forms (topology of modular varieties and trace formulas for Hecke correspondences), representation theory (Springer theory and Kazhdan-Lusztig theory), and algebraic geometry (topology of algebraic varieties).