Seminars Sorted by Series

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...

Abstract: This will be a summary of the closed discussions and an opportunity for everyone to contribute suggestions.

Abstract: This will be a broad talk about coherence of groups, and how it relates to conjectures about hyperbolic groups with planar boundaries. A group is coherent if every finitely generated subgroup is finitely presented. This is a property...

Abstract: There seems to be an analogy between the classes of fundamental groups of compact 3-manifolds and of one-relator groups. (Indeed, many 3-manifold groups are also one-relator groups.) For instance, Dehn’s Lemma for 3-manifolds (proved by...

Abstract: I will survey (in)coherence of lattices in semisimple Lie groups, with a view toward open problems and connections with the geometry of locally symmetric spaces. Particular focus will be placed on rank one lattices, where I will discuss...

Agenda: https://www.ias.edu/math/emerging-topics-working-group-nodal-sets-eigenfunctions

Agenda: https://www.ias.edu/math/emerging-topics-working-group-nodal-sets-eigen…

Agenda: https://www.ias.edu/math/emerging-topics-working-group-nodal-sets-eigen…

Agenda: https://www.ias.edu/math/emerging-topics-working-group-nodal-sets-eigen…

This talk will cover sections 2 and 3 of "The symplectic arc algebra is formal" by Abouzaid-Smith

This talk will prove formality results for Fukaya categories in some examples following "The symplectic arc algebra is formal" by Abouzaid--Smith.

This talk is an introduction to the work of Witten on physical approaches to knots, especially based on hep-th 1101.3216. Classical approaches to the Jones polynomial are based on various combinatorial constructions which have the downside of not...

Consider $T^*P^1$ as the B-model of a mirror equivalence. It turns out that the A-model mirror depends on choices and I will describe two of these mirrors: one with underlying symplectic manifold the complement of a conic in $T^*S^2$, and the other...

I will discuss Lipshitz and Sarkar's space level refinement of Khovanov homology. Their approach is combinatorial in nature and is inspired by Cohen-Segal-Jones' construction for Floer homology.

We'll talk about various dimensional reductions of the HW equations and the connections to (de)categorification as we continue explaining their physical origins. Time permitting we will discuss (conjectural?) relations to Fukaya-Seidel categories.