# Nasrin Altafi: Rank matrices and Jordan types for Artinian Gorenstein algebras

**Time: **
Mon 2020-12-14 15.00 - 16.00

**Lecturer: **
Nasrin Altafi

**Location: **
Zoom, meeting ID: 614 2389 6910

### Abstract

Rank matrices of linear forms for graded Artinian algebras represent the ranks of multiplication maps in different degrees. Rank matrices are in 1-1 correspondence to Jordan degree types. I will introduce the rank matrices and explain their connection to Jordan degree types and Lefschetz properties.

I will explain the necessary conditions for square matrices to be the rank matrices for Artinian Gorenstein algebras. For Artinian Gorenstein algebras of codimension three, I will classify rank matrices for linear forms with vanishing third power.

#### Notes

Meeting password: min {n | n = a^3+b^3=c^3+d^3, a,b,c,d \in N, {a,b} \neq {b,c}}