COLLOQUIUM
DEPARTMENT OF MATHEMATICS AND STATISTICS
OAKLAND UNIVERSITY
ROCHESTER, MICHIGAN 48309
Li Li
Oakland University
Combinatorial Aspects of Singularities in Algebraic Geometry
Abstract
In local theory of geometry, there has been substantial interest in understanding singularity that is related to the geometric objects with natural combinatorial structures. The geometric objects that we are interested in this talk include Hilbert schemes and Schubert varieties. The aim of the talk is to survey certain combinatorial aspects of such singularities, namely the q,t-analogue of Catalan numbers, and the q-analogue of Hilbert-Samuel multiplicities. Using methods in algebra and geometry, we obtain new relation between q,t-Catalan numbers and partition numbers, and new relation between Hilbert-Samuel multiplicities and Kazhdan-Lusztig polynomials.
Tuesday, November 1, 2011
3:00– 4:00 P.M.
372 Science and Engineering Building
(Refreshments at 2:30-3:00 PM in the kitchen area adjacent to 368 SEB)