**Date/Time**

Date(s) - 16/02/2023*10:30 am - 11:30 am*

**Thursday, February 16, 2023****10:30 – 11:30 am**

**Speaker:** Nasrin Altafi

**Title: ** *Hilbert functions and Lefschetz properties of graded Artinian Gorenstein algebras*

**Abstract:**A graded Artinian algebra is said to satisfy the strong Lefschetz property (SLP) if multiplication by all powers of a general linear form has maximal rank in every degree and if this property holds for the first power the algebra has the weak Lefschetz property (WLP). Determining the Lefschetz properties for Artinian algebras is motivated by the Hard Lefschetz Theorem. It shows that the cohomology rings of smooth projective varieties satisfy the SLP. Artinian Gorenstein algebras are the algebraic analog of these cohomology rings. In this talk, after providing some background material on the subject, we’ll prove that a generic Artinian Gorenstein quotient of coordinate rings of smooth points $Xsubset mathbb{P}^n$ has the SLP. This result provides a complete classification of the Hilbert functions of graded Artinian Gorenstein algebras that satisfy the SLP generalizing a result by T. Harima from 1995.

**Location: **Hamilton Hall, Room 207