**abstract:**
We introduce Lagrange spectra for translation surfaces,
generalizing the classical Lagrange spectrum. Several generalizations
of the classical Lagrange spectrum exist in the literature, defined in
terms of some flow in parameter space and satisfying some basic
properties: the existence of an Hall's ray, the closedness of the
spectrum and the density of values coming from periodic orbits. We
focus on these properties for the Teichmuller flow on closed an
SL(2,R)-invariant subsets of the moduli space of translation surfaces.
We prove two explicit formulae that allow to compute the spectra in
terms of two continued fraction algorithms: the first is a
skew-product over the classical continued fraction, which applies to
arithmetic Teichmuller discs, the second is the so-called Rauzy-Veech
induction, which applies to strata of translation surfaces, and, up to
some extent, also to any affine invariant locus. This is joint work
with Pascal Hubert and Corinna Ulcigrai.

Fri 14 Jun, 9:10 - 10:00, Aula Dini

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