NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR


Stephen Hermes

(Brandeis University)
  Surface Cluster Algebras and Cohomology of Mapping Class Groups

ABSTRACT: To an oriented surface with marked points, we can associate two algebraic objects: the cluster algebra and the cohomology ring of the mapping class group of the surface.  In the mid '90s, Kontsevich used a certain combinatorial model (the space of ribbon graphs) to construct cohomology classes for the mapping class group.  The surface cluster algebras of Fomin-Shapiro-Thurston can be used to study these cohomology classes, and construct combinatorial formulas for them.  We
will compute a certain graph on the surface of genus 2 that can be used to explicitly compute these cohomology classes.

October 7, 2011
10:30 - 11:30
511 Lake Hall

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