**abstract:**
Interval exchange transformations (I.E.T.s) are piecewise isometries of an interval to itself, with finitely many discontinuities. They generalize naturally rotations on the circle.

I will present two results on homogeneous diophantine approximations for I.E.T.s. The first result determines the relation between these approximations and the so-called *Rauzy-Veech algorithm*, a continued fraction procedure for I.E.T.s. The second result generalizes classical Khinchin
Theorem to I.E.T.s.

Diophantine conditions for I.E.T.s are strictly related to the *Teichmuller flow* on strata of abelian differentials. In particular Khinchin Theorem for I.E.T.s implies a sharp estimate on how fast a typical Teichm"uller geodesic wanders
towards infinity in its stratum. An interesting corollary is the extension of

Masur's logarithmic law

to strata of abelian differentials.

Tue 15 Mar, 14:30 - 15:30, Sala Conferenze Centro De Giorgi

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