Speaker: Ed Swartz, Cornell University

Title: Face enumeration on manifolds

Abstract: It has been over 100 years since Poincaré's original papers on the topological invariance of the Euler characteristic. What have we learned about the face numbers, (f_0, f_1, …, f_d), where f_i is the number of i-dimensional faces, of triangulated manifolds since then? The answer is astonishingly little. For instance, there is no manifold of dimension five or above for which the face numbers of all possible triangulations are known. We will survey various aspects of what has been discovered since Poincaré. Along the way we will see how the introduction of commutative algebra revolutionized the subject in the 70's and has led to several recent results.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491