**Date & Time:** Monday, August 31, 2009, 15:30-16:30.

**Venue:** Committee Room

**Title:** Ideals of Analytic Deviation One and Test Modules

**Speaker:** Ganesh Kadu, IIT Bombay

**Abstract:** Let *R* be a Cohen-Macaulay local ring of dimension *d* and *M* be a maximal Cohen-Macaulay *R*-module. Let *I* be an ideal of analytic deviation one and analytic spread *d*. We study the function
whenever this length is finite. We give two natural conditions when this length becomes finite. The function *f(n)* is given by a polynomial for large values of *n* of degree at most *d-1*. It is of some interest to find the degree of this polynomial. We show that when the degree of this polynomial is less than *d-1* then the fiber module *F(I,M)* is free over the fiber cone *F(I)*.

I will also talk about some results on graded local cohomology modules and a generalization of Grothendieck-Serre difference formula.