Date & Time: Friday, January 24, 2013, 15:00-16:00.
Venue: Ramanujan Hall
Title: Towards a Resolution of Powers of Determinantal Ideals
Speaker: Hema Srinivasan, University of Missouri
Abstract: Let $X$ be an $m\times n$ matrix with entries in a ring $R$. Then the ideal of $t\times t$ minors, denoted by $I_t(X)$ is called a determinantal ideal. It is well known that the height of $I_t(X)$ is at most $(m-t+1)(n-t+1)$ and the resolution of $R/I_t$ in characteristic zero is known for all $t$ and characteristic free description for the ideal of maximal and submaximal minors are known by the works of Eagon, Northcott, Buchsbaum, Akin, Weyman and Lasoux. However, not much is known about the resolution for the powers of these ideals. We will discuss the resolutions of $R/I_t$ and $R/(I_t)^2$ when $X$ is a square matrix of size less than $t+2$.