2010-02-12

Vladimir Retakh (Rutgers University)

From Factorizations of Noncommutative Polynomials to Combinatorial Topology

In prelude to this lecture, I will say a few words about Israel Gelfand (who passed away in October 2009) and his legendary Seminar. In the main part, I will give a survey of an area originated by Gelfand and the speaker around 1995. I will associate to a directed graph (ranked quiver) a noncommutative algebra and a certain polynomial over this algebra together with its factorizations. To any cell complex there corresponds such a quiver and, therefore, the noncommutative algebra. I will discuss connections between the properties of the algebra and the topological structure of the complex.