Date & Time: Tuesday, July 13, 2010, 16:00-17:00.
Venue: Ramanujan Hall
Title: Arithmetic Rank of Ideals
Speaker: Manoj Kummini, Purdue University
Abstract: The arithmetic rank of an ideal $I$ (denoted $\mathrm{ara} I$) in a polynomial ring $R = \Bbbk[x_1, \ldots, x_n]$ is the least number $r$ such that there exists polynomials $f_1, \ldots, f_r$ such that the ideals $(f_1, \ldots, f_r)$ and $I$ have the same radical. It is the least number of equations to required to define the variety of $I$. We will discuss its relation to syzygies and some combinatorial constructions that have been used to determine the arithmetic rank of some classes of monomial ideals.