## Quantum Topology / Hopf Algebra Seminar

Sergei Chmutov

Ohio State University

Generalized duality for graphs on surfaces and its application to links.

**Abstract:**The natural duality of graphs embedded into a surface can be generalized to a duality with respect to a subset of edges. The dual graph might be embedded into a different surface. For graphs on surfaces there is a generalization of the classical Tutte polynomial called the Bollobas-Riordan polynomial. In this talk I will explain a relation between the signed Bollobas-Riordan polynomials of dual graphs. This relation unifies various recent Thistlethwaite's type results of expressing the Jones polynomial of (virtual) links as specializations of the Bollobas-Riordan polynomials.

Tuesday January 15, 2008 at 2:00 PM in SEO 512