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Cluster algebras and Knot Theory

Ralf Schiffler (U. of Connecticut)

Location:  Zoom
Date & time: Wednesday, 16 February 2022 at 3:30PM - 4:30PM

Abstract:  Cluster algebras are commutative algebras with a special combinatorial structure. They were introduced in 2002 by Sergey Fomin and Andrei Zelevinsky in the context of canonical bases in Lie theory and have quickly developed deep connections to other areas of mathematics and physics. Cluster algebras are subalgebras (over the integers) of a field of rational functions in several variables, and they are defined by specifying a set of generators, the cluster variables, inside this field. The cluster variables are constructed recursively via a combinatorial procedure called mutation which is governed by the choice of an initial quiver (or oriented graph). 

In this talk, I will focus on a recent development providing a relation between cluster algebras and knot theory. To every knot (or link) diagram one can associate a cluster algebra in which one finds a special set of cluster variables, each of which recovers the Alexander polynomial of the knot.  

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