Event time:
Tuesday, February 25, 2025 - 4:00pm
Location:
KT 207
Speaker:
Changjie Chen
Speaker affiliation:
CRM - Université de Montreal
Event description:
It is known that the systole function, defined to be the length of a shortest closed geodesic, is topologically Morse on the moduli space of Riemann/hyperbolic surfaces, proved by Hugo Akrout. However, Morse theory cannot be applied as the function is not differentiable and the base space is noncompact.
We construct a family of weighted exponential averages of all geodesic-length functions, and show that they are Morse on the Deligne-Mumford compactification of the moduli space. We will also characterize the critical points and Morse indices, and from certain properties of them we may find conclusions on the homology of the moduli space by Morse theory.