EVENT DETAILS AND ABSTRACT

Title: Moduli spaces, noncommutative geometry and characteristic classes.
Speaker: Alastair Hamilton
Speaker Info: Texas Tech
Brief Description:
Special Note:
Abstract:

In this introductory talk I will explain a well-known result of Kontsevich which links the homology of the moduli space of Riemann surfaces to the homology of a certain Lie algebra that he constructed as a noncommutative analogue of the Poisson algebra of Hamiltonian vector fields on an affine symplectic manifold. I will introduce some basic notions, such as:

(1) Ribbon graphs and their role in the decomposition of the moduli space of Riemann surfaces.

(2) Chevalley-Eilenberg homology of differential graded Lie algebras.

(3) Maurer-Cartan elements and their characteristic classes.