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

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).