Combinatorics, Algebra, & Topology Seminar

Fall 2018

All talks are from 1200-1300 in the designated room unless otherwise specified.

• Nov

  08
• The strong Lefschetz property for Artin Gorenstein algebras associated to matroids

  Yasuhide Numata

  Shinshu University

  Time: 12:00 PM

  View Abstract

  We consider a certain class of finite-dimensional Gorenstein algebras associated to matroids. We show the Lefschetz property in the case where the matroid corresponds to a modular geometric lattice. Our result implies that the modular geometric lattice has the Sperner property. We also discuss the Grobner fan of the defining ideal of our Gorenstein algebra.

• Oct

  29
• Joseph Kung

  University of North Texas

  Location: CH351

  Time: 12:00 PM

• Oct

  19
• Partition Counting, Dynkin diagrams, quantum dilogarithms, and generalizations

  Justin Allman

  USNA

  Location: CH225

  Time: 12:00 PM

  View Abstract

  The Durfee's square identity is an effective way to iteratively count partitions going back to at least Cauchy. In this talk we show how this identity is related to representations of a certain quiver, namely an orientation of the A_2 Dynkin diagram. Furthermore, we show that identities among quantum dilogarithm series, with a rich history in their own right, can encode infinitely all of the Durfee's-square-type identities simultaneously. Finally, we discuss how these identities generalize to entire families of quivers.