NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR



Nathan Reading

(North Carolina State University)


  Mutation-Linear Algebra

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.

April 5, 2013
10:00 - 11:00
(Notice unusual time)
511 Lake Hall


For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky alexmart >at< neu >dot< edu