Previous Conferences & Workshops

S-operators were originally introduced by V. Lafforgue as certain operators acting on the cohomology of moduli of Shtukas. I will discuss their analogues and generalizations in the Shimura variety setting. They induce Hecke equivariant maps between...

Abstract: Consider a completely integrable symplectic twist map of the two dimensional annulus: then the invariant curves make a partition of the annulus and they are vertically ordered by their rotation number. Here we raise a similar question in...

Datasets are often used multiple times with each successive analysis depending on the outcomes of previous analyses on the same dataset. Standard techniques for ensuring generalization and statistical validity do not account for this adaptive...

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...

Hyperbolic 3-manifolds with arithmetic fundamental group exhibit many remarkable number theoretic properties. Is it possible that such manifolds live over finite fields (whatever that means)? In this talk I will give some evidence for this...

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...

The analytic theory of Poincaré series and Maass cusp forms and their L-functions for $SL(3,Z)$ has, so far, been limited to the spherical Maass forms, i.e. elements of a spectral basis for $L^2(SL(3,Z)\PSL(3,R)/SO(3,R))$. I will describe the Maass...

Abstract: We consider the problem whether small perturbations of integrable mechanical systems can have very large effects. It is known that in many cases, the effects of the perturbations average out, but there are exceptional cases (resonances)...