### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

FEBRUARY 12, 2016

**Speaker: **
Steve Halperin, University of Maryland

**Title: ***
Lie algebras and the rational homotopy groups of a topological space
*

**Abstract:**
The higher homotopy groups of a topological space X are abelian, and when tensored with the rationals define a graded Lie algebra, L. When X is a finite polyhedron, or more generally, if X has finite Lusternik-Schnirelmann catgory, then over the last 30 years Sullivanâ€™s minimal model theory has provided strong structural results for this Lie algebra and for the fundamental group. I will describe some of these, both older and very recent, as well as some of the basic ideas which go into the proofs.

**Time:** Friday, February 12, 2016, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

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