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ISM Discovery School on Mutations 
(Montréal, Canada, July 4-8th, 2022)

Mutations: From Cluster Algebras to Representation Theory

Organizers: Thomas Brüstle, Kaveh Mousavand, Charles Paquette

Theme & Objectives:

The theory of cluster algebras, introduced by Fomin and Zelevinsky in 2000, has been one of the most active areas of research in Mathematics in the current century. Over the last 20 years, cluster algebras have established numerous connections to different disciplines, including with representation theory. This is particularly because the notion of mutation appears in many different contexts  (such as in the classical tilting theory). Thanks to these connections and recent developments in representation theory (such as tau-tilting theory), mutation has an even deeper significance in this domain: one can mutate tau-tilting objects, functorially finite torsion classes, left finite wide subcategories, etc. These mutations are also related to the wall-crossing phenomenon in the study of stability conditions, known as wall-and-chamber structure. 

In this ISM discovery school, our aim would be to explore different topics in representation theory through the lens of mutations. Moreover, we highlight the profound connections between these incarnations of the mutation phenomenon in the following mini-courses, which will be supplemented by some research talks:

  1. Mutations in representation theory (by Lidia Angeleri Hügel);

  2. Stability conditions in representation theory (by Sota Asai);

  3. Lattice-theoretical and combinatorial aspects of tau-tilting (by Hugh Thomas).

Research Talks

In addition to the mini-courses, there will be some research talks given by experts that supplement the mini-courses. Our list of speakers includes​

  • Nathan Reading (North Carolina State University)

  • Hipolito Treffinger (Université Paris Cité)

  • Ralf Schiffler (University of Connecticut)

Collaborative Research

During the school, the participants with closer research interests will be divided into smaller subgroups and discuss some research problems related to the theme of this school. Each group will have one or two experts who lead the collective discussions.

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