**Speaker:** Nathan Reading

**Title:** Mutation-linear algebra

**Abstract:** Matrix mutation is a strange operation that takes one matrix and “mutates” it to produce another matrix of the same dimensions. This operation appeared in the definition of cluster algebras about a decade ago and has since been discovered in seemingly different areas of mathematics. Given *n* x *n* matrix, the operation of mutation also defines a family of piecewise-linear maps on ℝ* ^{n}*. Mutation-linear algebra is the study of linear relations that are preserved under these “mutation maps.”

This talk is meant as a gentle introduction to cluster algebras and to mutation-linear algebra. The goals of the talk are threefold:

1. To motivate cluster algebras (and thus matrix mutation) by examples and by discussing/mentioning the many areas where cluster algebras seem to be relevant.

2. To motivate mutation-linear algebra in terms of cluster algebras.

3. To consider the mutation-linear-algebraic notion of basis in small examples, and in examples related to the geometry of surfaces.