Ï㽶ÊÓƵ

Title: Morse functions on the moduli space of hyperbolic surfaces

Abstract: In theory one can find a Morse function on the moduli space M_{g,n} of hyperbolic surfaces of genus g with n punctures, as Morse functions on a given manifold/orbifold are dense among all smooth functions. However, it may not be so easy to find a ‘natural’ one.

I will talk about my construction, which improves the known results from topological Morse functions on M_{g,n}, i.e., the systole function, to C^2-Morse functions (and eventually smooth ones) on the Deligne-Mumford compactification M_{g,n} bar.

I will start by talking about some background of hyperbolic geometry, Teichmüller theory and Morse theory.

Ìý