# Koszul Algebras and Algebraic Topology

SPEAKER: Brad Shelton

TITLE: Koszul Algebras and Algebraic Topology

ABSTRACT A large class of quadratic algebras was introduced in 2005 by Retakh, Serconek and Wilson, generalizing an earlier construction of Gelfand, Retakh and Wilson. A mistake in the literature suggests that all such algebras are Koszul. This was disproved by Cassidy and S in 2007. We now have strong results on when the algebras are Koszul, expressed in terms of topological data. To do this we must introduce some new topological cohomology groups. These new cohomology groups may be of independent interest. (Joint work with T. Cassidy and C. Phan.)