School of Mathematics

https://www.ias.edu/math/wam/2017

https://www.ias.edu/math/wam/2017

At the November workshop, I described a new algorithm to cover compact, congruence locally symmetric spaces by balls. I’ll discuss how to compute the nerve of such a covering and Hecke actions on its cohomology. Joint work with Aurel Page.At the...

For given a Lagrangian in a symplectic manifold, one can consider deformation of A-infinity algebra structures on its Floer complex by degree 1 elements satisfying the Maurer-Cartan equation. The space of such degree 1 elements can be thought of as...

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.

Dadush and...

Polynomial optimization over hypercubes has important applications in combinatorial optimization. We develop a symmetry-reduction method that finds sums of squares certificates for non-negative symmetric polynomials over k-subset hypercubes that...

Abstract: Consider the defocusing cubic Schrödinger equation defined in the 2 dimensional torus. It has as a subsystem the one dimension cubic NLS (just considering solutions depending on one variable). The 1D equation is integrable and admits...

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...

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...

In this talk, we consider the problem of explicitly constructing a binary tree code with constant distance and constant alphabet size. We present an explicit binary tree code with constant distance and alphabet size polylog(n), where n is the depth...