Seminars Sorted by Series

Deep learning has led to rapid progress in open problems of artificial intelligence—recognizing images, playing Go, driving cars, automating translation between languages—and has triggered a new gold rush in the tech sector. But some scientists...

Last Fall the Emerging Topics on Scalar Curvature and Convergence groupdiscussed and devised a number of conjectures concerning the intrinsic flat limits of sequences of manifolds with lower bounds on their scalar curvature. Many of thesewere almost...

Abstract: We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete computation of several...

Abstract: We first examine the existence, uniqueness, regularity, twist and symplectic properties of compact invariant cylinders with boundary, located near simple or double resonances in perturbations of action-angle systems on the annulus $A^3$...

Abstract: In this talk we present a general shadowing result for normally hyperbolic invariant manifolds. The result does not use the existence of invariant objects like tori inside the manifold and works in very general settings. We apply this...

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)...

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...

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: 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: 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...