Using templates to study problems in dynamics and number theory

Abstract: Templates may be viewed as a combinatorial device that helps study asymptotic properties of lattice successive minima. This simple idea, introduced in joint work with Lior Fishman, David Simmons, and Mariusz Urbanski, promises to be useful in several areas beyond our current applications. The latter lie at the fertile interface along Dani’s correspondence principle between Diophantine approximation and homogeneous flows, deepened by Kleinbock & Margulis; and Schmidt & Summerer’s parametric geometry of numbers, deepened by Roy. Templates are at the heart of our variational principle (arXiv:1901.06602), which provides a unified framework to compute the Hausdorff and packing dimensions of a variety of sets of dynamical and number-theoretic interest. We will introduce and give some flavor for our project, hint at a few new directions, and hope to present several open problems of varying depth to reward participants of this wonderful seminar!

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar