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 ℝn. 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.