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On the Lagrange spectrum of moduli spaces of Riemann surfaces $M_{g,n}$

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Speaker: 
Vincent Delecroix
Affiliation: 
Université Bordeaux 1/MPIM
Date: 
Tue, 2018-11-13 12:00 - 13:00
Location: 
MPIM Lecture Hall

We consider the moduli space $M_{g,n}$ of Riemann surfaces of
genus g with n punctures endowed with the Teichmueller metric.
The Teichmueller geodesic flow is a non-uniformly hyperbolic
flow on $M_{g,n}$ (with respect to the Masur-Veech measure). The
Lagrange spectrum of $M_{g,n}$ is a closed subset of the positive
real numbers that measures how closed geodesics escape $(M_{g,n}$ is
not compact). The classical Lagrange spectrum corresponds to the
case of $M_{1,1}$ and is motivated by diophantine approximations.
We will show that some properties of the classical Lagrange
spectrum extends to the Lagrange spectrum of any $M_{g,n}$. But most
of it remains mysterious.

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