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From cluster algebras to representation theory and back

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CAR - Cluster algebras and representation theory

In the last twenty years we have been witness to the fruitful interplay between representation theory of quivers and cluster algebras. On the one hand, representation theory has been a very powerful tool to categorify cluster algebras. On the other hand, the study of cluster algebras has unveiled phenomena that are now central in representation theory, such as tau-tilting theory or higher homological algebra. 

In this talk, which is based on joint work in progress with Nathan Ilten and Alfredo Nájera, I will explain how one can use deformation theory to construct cluster algebras of finite type from (the dual of) their exchange graph using deformation theory. Time permitting I will mention how this process can be generalised to tau-tilting finite algebras. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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