Binghamton University


MATHEMATICAL SCIENCES
COLLOQUIUM


DATE: Friday, April 12, 2002
TIME: 4:30 - 5:30 PM
PLACE: LN 2205
SPEAKER: Richard Pollack, NYU Courant
TITLE: On the Betti Numbers of Semi-Algebraic Sets

Abstract


A classic result in real algebraic geometry, due to Oleinik-Petrovsky, Thom, and Milnor, bounds the topological complexity (the sum of the Betti numbers) of basic semi-algebraic sets. These bounds are used in many applications -- for instance, for proving tight lower bounds on the complexity of several problems in computer science. Over the past few years there have been several improvements and generalizations of this bound due to Basu, Basu-Pollack-Roy, and Pollack-Roy. In particular, it is now possible to prove better bounds on the individual Betti numbers of semi-algebraic sets rather than their sum. The talk will be a survey of these results.

R E F R E S H M E N T S

4:00 To 4:25 PM
Kenneth W. Anderson
Memorial Reading Room