## Speaker:

Amir Vig

## Speaker Link:

## Institution:

University of Michigan

## Time:

Tuesday, October 29, 2024 - 11:00am

## Host:

## Location:

Rowland Hall 340P

For planar billiard tables, the marked length spectrum encodes the lengths

of action (minus the length) minimizing orbits of a given rational rotation

number. For strictly convex tables, a renormalization of these lengths extends

to a continuous function called Mather’s beta function or the mean minimal

action. We show that using the algebraic structure of its Taylor coefficients,

one can prove C infinity compactness of marked length isospectral sets. This

gives a dynamical counterpart to the Laplace spectral results of Melrose,

Osgood, Phillips and Sarnak.