Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Hilbert series of algebras associated to direct graphs and order homology

Speaker: **Vladimir Retakh**, Rutgers University

Date: Thursday, March 24, 2011 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of homological properties of the graphs. We use our results to construct algebras with a prescribed Hilbert series. (Joint work with Shirlei Serconek and Robert Wilson.)