### The Hausdorff dimension of not uniquely ergodic 4-IETs has codimension 1/2.

Chaika, J *(University of Utah)*

Tuesday 01 July 2014, 09:00-09:50

Seminar Room 1, Newton Institute

#### Abstract

The main results of this talk are:
a) The Hausdorff dimension of not-uniquely 4-IETs is 2 1/2 as a subset of
the 3 dimensional simplex
b) The Hausdorff dimension of flat surfaces in H(2) whose vertical flow is
not uniquely ergodic is 7 1/2 as a subset of an 8 dimensional space
c) For almost every flat surface in H(2) the set of directions where the
flow is
not uniquely ergodic has Hausdorff dimension 1/2.
These results all say that the Hausdorff codimension of these exceptional
sets is 1/2. Masur-Smillie showed that the Hausdorff codimension was less
than 1. It follows from work of Masur that the Hausdorff codimension is at
least 1/2. This is joint work with J. Athreya.

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