**Date & Time:** Wednesday, January 07, 2009, 14:30-15:30.

**Venue:** Ramanujan Hall

**Title:** Jet Schemes of Some Matrix-Related Varieties

**Speaker:** Bharath Sethuraman, California State University, Northridge

**Abstract:** We discuss an open problem in commuting matrices and describe how jet schemes of some matrix related varieties arise naturally in this setting. Jet schemes are the analogues for algebraic varieties of the notion of tangent (and higher order) bundles from differential geometry. We describe some results on the irreducibility of jet schemes of determinantal varieties and jet schemes of the commuting matrix pairs scheme, and also describe some combinatorial results on shellability of simplicial complexes attached to one of these jet schemes.