Wednesday, June 19

8:30 AM

Mudd Hall Auditorium

Chair: To be determined

## IP5

Convex Polytopes and Enumeration

The study of convex polytopes _ a convex polytope is the convex hull of finitely many points in Euclidean space _ has enjoyed a great deal of attention from the perspective of a variety of subjects, such as geometry, combinatorics, and optimization. In recent years, the discovery of remarkable connections with commutative algebra and algebraic geometry led to solutions of several major problems as well as to new research directions.
The speaker will present a sample of landmark results and problems of current interest, focusing on enumerative questions pertaining to polytopes and enumerative questions concerning other combinatorial objects_ such as permutations, partitions, and graphs _ in which (rather unexpectedly) polytopes arise.
**Rodica Simion**

Department of Mathematics

George Washington University

*MEM, 4/10/96*