Gabriel Rivière


Université de Nantes


Thursday, December 2, 2021 - 11:00am to 11:50am



Zoom ID: 949 5980 5461, Password: the last four digits of ID in the reverse order

Poincaré series are natural functions that arise in Riemannian geometry 
when one wants to count the number of geodesic arcs of length less than 
T between two given points on a compact manifold. I will begin with an 
introduction on this topic. Then I will discuss some recent results with 
N.V. Dang (Univ. Paris Sorbonne) showing that, in the case of negatively 
curved manifolds, these series have a meromorphic continuation to the 
whole complex plane. This can be shown by relating Poincaré series with 
the resolvent of the geodesic vector field and by exploiting recent 
results on this resolvent obtained through microlocal methods. If time 
permits, I will also explain how the genus of a surface can be recovered 
from the analysis of these series.