## Seminars and Colloquia by Series

Friday, October 13, 2017 - 15:00 , Location: Skiles 154 , Bhanu Kumar , GT Math , Organizer: Jiaqi Yang
Birkhoff's Theorem is a result useful in characterizing the boundary of certain open sets U ⊂ T^1 x [0, inf) which are invariant under "vertical-tilting" homeomorphisms H. We present the method used by A. Fathi to prove Birkhoff's theorem, which develops a series of lemmas using topological arguments to prove that this boundary is a graph.
Friday, October 6, 2017 - 15:00 , Location: Skiles 154 , Sergio Mayorga , Georgia Tech , Organizer: Jiaqi Yang
We will look at a system of hamiltonian equations on the torus, with an initial condition in momentum and a terminal condition in position, that arises in mean field game theory. Existence of and uniqueness of solutions will be shown, and a few remarks will be made in regard to its connection to the minimization problem of a cost functional. This is the second part of lasrt week's talk.
Friday, October 6, 2017 - 15:00 , Location: Skiles 154 , Prof. Rafael de la Llave , School of Mathematics, Georgia Tech , Organizer: Jiaqi Yang
We will present an introduction to the results of S. Aubry and J. Mather who used variational methods to prove the existence of quasi-periodic orbits in twist mappings and in some models appearing in solid state Physics.
Friday, September 29, 2017 - 15:00 , Location: Skiles 154 , Sergio Mayorga , Georgia Tech , Organizer: Jiaqi Yang
We will look at a system of hamiltonian equations on the torus, with an initial condition in momentum and a terminal condition in position, that arises in mean field game theory. Existence of and uniqueness of solutions will be shown, and a few remarks will be made in regard to its connection to the minimization problem of a cost functional.
Friday, September 22, 2017 - 15:00 , Location: Skiles 154 , Jiaqi Yang , Georgia Tech , Organizer: Jiaqi Yang
We will continue from last week's talk. There are many advances toward proof of Arnold diffusion in Mather's setting. In particular, we will study an approach based on recent work of Marian-Gidea and Jean-Pierre Marco.
Friday, September 15, 2017 - 15:00 , Location: Skiles 154 , Jiaqi Yang , Georgia Tech , Organizer: Jiaqi Yang
We will introduce Arnold diffusion in Mather's setting. There are many advances toward proof of this. In particular, we will study an approach based on recent work of Marian-Gidea and Jean-Pierre Marco.
Friday, April 21, 2017 - 15:00 , Location: Skiles 254 , Adrian P. Bustamante , Georgia Tech , Organizer:
A classical theorem of Arnold, Moser shows that in analytic  families of maps close to a rotation we can find maps which are smoothly conjugate to rotations. This is one of the first examples of the KAM theory. We aim to present an efficient numerical algorithm, and its implementation, which approximate the conjugations given by the Theorem
Friday, April 7, 2017 - 15:05 , Location: Skiles 254 , Prof. Rafael de la Llave , School of Math, Georgia Tech , Organizer: Jiaqi Yang
It is well known  that periodic orbits give all the information about dynamical systems, at least for expanding maps, for which the periodic orbits are dense. This turns out to be true in dimensions 1 and 2, and false in dimension 4 or higher.We will present a proof  that  two $C^\infty$ expanding maps of the circle, which are topologically equivalent are $C^\infty$ conjugate if and only if the derivatives or the return map at periodic orbits are the same.
Friday, March 31, 2017 - 15:05 , Location: Skiles 254 , Lei Zhang , School of Mathematics, GT , Organizer: Jiaqi Yang
In this talk, we will give an introduction to the variational approach to dynamical systems. Specifically, we will discuss twist maps and prove the classical results that area-preserving twist map has Birkhoff periodic orbits for each rational rotation number.
Friday, March 10, 2017 - 15:00 , Location: Skiles 254 , Rafael de la Llave , GT Math , Organizer: Rafael de la Llave
A classical theorem of Arnold, Moser shows that in analytic  families of maps close to a rotation we can find maps which are smoothly conjugate to rotations. This is one of the first examples of the KAM theory. We aim to present a self-contained version of Moser's proof and also to present some efficient numerical algorithms.