**Date & Time:** Monday, July 04, 2016, 10:30-11:30.

**Venue:** Ramanujan Hall

**Title:** On Unimodality of Hilbert Functions

**Speaker: ** Prof. Hema Srinivasan, University of Missouri

**Abstract:** Hilbert Function of a graded artin algebra is said to be unimodal if it increases (not necessarily strictly) from zero monotonically till it reaches its maximum value and then decreases ( again not necessarily strictly) till it reaches zero. The notion of unmorality can be imagined because the Gorenstein Artin algebras have symmetric Hilbert functions. However, it is known that unmodality is not always there even for Gorenstein algebras starting at codimension five. In this talk we consider this problem for low codimension Gorenstein and level algebras and prove it in many of the instances.