Singularities arising from cluster algebras of finite type

Eleonore FABER
University of Leeds

Date(s) : 21/10/2021   iCal
14 h 00 min - 15 h 00 min

Cluster algebras were introducted by Fomin and Zelevinsky in the context of total positivity in Lie theory. Since then, cluster structures have appeared in many different contexts, ranging from representation theory and combinatorics to mirror symmetry.

In this talk, I will first give a short introduction to cluster algebras and then focus on the class of cluster algebras of finite type, which are classified by Dynkin diagrams. We study these commutative algebras from the point of view of singularity theory: we classify their singularities and develop constructive resolutions of these singularities over fields of arbitrary characteristics. From the same perspective, we study cluster algebras coming from a star shaped quiver, which are not of finite type, but whose singularities exhibit interesting combinatorial phenomena. This is joint work with Angélica Benito, Hussein Mourtada, and Bernd Schober.



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