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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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