**Date & Time:** Friday, January 16, 2009, 11:30-12:30.

**Venue:** Ramanujan Hall

**Title:** On the Chern Number of an Ideal

**Speaker:** Mousumi Mandal, IIT Bombay

**Abstract:** It is shown that for a parameter ideal *J* of a finitely generated module *M* over a local ring, the chern number *e _{1}(J,M)&le 0*. Vasconcelos' Negativity Conjecture has been settled for certain unmixed quotients of regular local rings by explicitly finding the Hilbert polynomial of any parameter ideal in a local ring

*S/I*where (

*S*,

**n**) is a regular local ring and

*I = I*, where

_{1}&cap I_{2}&cap . . . &cap I_{r}*I = I*, are Cohen-Macaulay ideals of equal height and for all

_{1}, I_{2}, . . . ,I_{r}*i = j, I*are

_{i}+ I_{j}**n**-primary. Goto's solution to Vasconcelos' negativity conjecture has been presented. i.e., if

*R*is a Noetherian local ring of positive dimension and

*Q*is a parameter ideal, then

*R*is Cohen-Macaulay if and only if

*R*is unmixed and

*e*.

_{1}(Q)=0