Published on *Max-Planck-Institut für Mathematik* (https://www.mpim-bonn.mpg.de)

Posted in

- Vortrag [1]

Speaker:

Vincent Delecroix
Zugehörigkeit:

Université Bordeaux 1/MPIM
Datum:

Die, 2018-11-13 12:00 - 13:00 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.

**Links:**

[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/de/node/3444

[3] https://www.mpim-bonn.mpg.de/de/node/8825