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.