REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
Nathan Reading
ABSTRACT: Matrix mutation is an operation that takes a 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 an n by 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." I will start by quickly reviewing the definition of a cluster algebra. I will then motivate mutation-linear algebra by discussing universal coefficients of cluster algebras. Finally, I will consider the mutation-linear-algebraic notion of "basis" in small examples, and in examples related to the geometry of surfaces.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu