Hodge theory of character varieties via Topological Quantum Field Theories
Date
Thursday, March 7, 2019 13:00 - 15:30
Speaker
Angel Gonzalez Prieto (Universidad Politécnica de Madrid)
Location
Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Tamas Hausel
Contact
Topological Quantum Field Theories are powerful categorical tools that provide deep insight into the behavior of topological invariants under gluing. In this talk, we will focus on their the applications to representation theory. Following this idea, we shall construct a lax monoidal TQFT that computes the class in the Grothendieck ring of algebraic varieties of the representation varieties over any compact manifold. This TQFT gives rise to a recursive pattern that can be exploited for creating an e_ective method of calculation. As application, we will use it to compute the virtual Hodge structure on the cohomology of SL(2;C)-character varieties.
Joint work with M. Logares and V. Munoz.