University of Toledo Department of Mathematics and Statistics

Geometry and Dynamics Seminar

March 16, 2020
Funda Gultepe
Title:Cluster Algebras from Surfaces, part II
Abstract: In this talk we will talk about triangulations, arc complex and other notions coming from surfaces and relate these to cluster algebras .
Related articles: Fomin,Shapiro,Thurston Cluster Algebras and Triangulated Surfaces.
Fomin,Shapiro,Thurston Cluster Algebras and Triangulated Surfaces II: Lambda Lengths.

March 2, 2020
Funda Gultepe
Title:Cluster Algebras from Surfaces
Abstract: In this talk we will associate quivers to triangulations on a surface and mutations to flips. We will definte these notions and see our previous examples of quivers in terms of surfaces and draw cluster algebras from them.
Related articles: Fomin,Shapiro,Thurston Cluster Algebras and Triangulated Surfaces.
Fomin,Shapiro,Thurston Cluster Algebras and Triangulated Surfaces II: Lambda Lengths.

February 24, 2020
Funda Gultepe
Introduction to Cluster Algebras
Abstract: I will give the definitions of basic concepts related to cluster algebras such as quiver, mutation and so on. I will give some examples and continue with defining cluster algebra and then introducing cluster algebras on surfaces.

February 17, 2020
Gerard Thompson
Title:A leisurely review of Lie Theory leading, maybe, to some ideas about Cluster Algebras, II
Abstract: This is continuation of the previous topic.

February 10, 2020
Gerard Thompson
Title:A leisurely review of Lie Theory leading, maybe, to some ideas about Cluster Algebras
Abstract: We review the main ideas of Lie Theory without assuming any previous knowledge. We will discuss the main types of Lie algebra and eventually discuss root systems as the key idea for classifying semi-simple Lie algebras. We will attempt to make connections with Robert Marsh's book on Cluster Algebras and outline some of the challenges involved.