### Special time: **Wednesday
January 18**, 2006, **3:30
PM**

#### tea at
3:15 PM at the Math Department lounge (Goldsmith 300)

**Speaker**: Alexander Bufetov (Chicago/Rice)

**Title**: Interval exchange transformations and Teichmüller flows

**Abstract**:
An interval exchange transformation is a piecewise isometry of
an interval, obtained by cutting the interval into a finite number of
subintervals, and then rearranging these subintervals according to a
given permutation.
Interval exchanges exhibit both deterministic and chaotic properties,
and we are still very far from a complete understanding of their
dynamical behaviour.

One of the main tools in the study of interval exchanges is
renormalization: the
first return map of an interval exchange on a smaller subinterval is
again an interval exchange. By choosing the smaller subinterval
appropriately, one endows the space of interval exchange transformations
with a measure-preserving dynamical system, called the Rauzy-Veech-Zorich
induction map. The dynamical behaviour of an interval exchange is then
encoded by the behaviour of its orbit under the induction map.

The main result of the talk is a stretched-exponential bound on the
speed of mixing for the induction map. A corollary of
the main result is the Central Limit Theorem for the Teichmüller
flow on the moduli space of abelian differentials with prescribed
singularities.

The talk, aimed at a general audience, would require no background.