Event Type:

Number Theory Seminar

Date/Time:

Tuesday, October 14, 2014 - 16:00 to 17:00

Location:

Kidder 236

Guest Speaker:

Institution:

University of Utah

Abstract:

The main results of this talk are: a) The Hausdorff dimension of the set 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.

Host: