## A Celebration of Freeman Dyson’s Maker of Patterns

Freeman Dyson

April 13, 2018

Freeman Dyson

April 13, 2018

Noah Stephens-Davidowitz

Visitor, School of Mathematics

April 17, 2018

We consider the following question: how many points with bounded norm can a "non-degenerate" lattice have. Here, by a "non-degenerate" lattice, we mean an n-dimensional lattice with no surprisingly dense lower-dimensional sublattices.

Annie Raymond

University of Massachusetts, Amherst

April 16, 2018

Marcel Guardia

UPC

April 12, 2018

Ke Zhang

University of Toronto

April 11, 2018

Abstract: Arnold diffusion studies the problem of topological instability in nearly integrable Hamiltonian systems. An important contribution was made my John Mather, who announced a result in two and a half degrees of freedom and developed deep theory for its proof. We describe a recent effort to better conceptualize the proof for Arnold diffusion.

Marian Gidea

Yeshiva University

April 11, 2018

Abstract: We consider a geometric framework that can be applied to prove the existence of drifting orbits in the Arnold diffusion problem. The main geometric objects that we consider are 3-dimensional normally hyperbolic invariant cylinders with boundary, which admit well-defined stable and unstable manifolds. These enable us to define chains of cylinders i.e., finite, ordered families of cylinders in which each cylinder admits homoclinic connections, and any two consecutive cylinders admit heteroclinic connections.