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Friday, February 24, 2017 - 15:05 ,
Location: Skiles 254 ,
Simon Berman ,
School of Physics ,
Organizer: Jiaqi Yang

In
a high harmonic generation (HHG) experiment, an intense laser pulse is
sent through an atomic gas, and some of that light is converted to very
high harmonics through the interaction with the gas. The spectrum of
the emitted light has a particular, nearly universal shape. In this
seminar, I will describe my efforts to derive a classical reduced
Hamiltonian model to capture this phenomenon. Beginning with a
parent Hamiltonian that yields the equations of motion for
a large collection of atoms interacting self-consistently with the
full electromagnetic field (Lorentz force law + Maxwell's equations), I
will follow a sequence of reductions that lead to a reduced
Hamiltonian which is computationally tractable yet should
still retain the essential physics. I will conclude by pointing out some
of the still-unresolved issues with the model, and if there's time I
will discuss the results of some preliminary numerical simulations.

Friday, January 20, 2017 - 03:05 ,
Location: Skiles 254 ,
Álex Haro ,
Univ. of Barcelona ,
Organizer:

We
will design a method to compute invariant tori in Hamiltonian systems
through the computation of invariant tori for time- T maps. We will also
consider isoenergetic cases (i..e. fixing energy).

Friday, November 11, 2016 - 15:05 ,
Location: Skiles 170 ,
Adrián P. Bustamante ,
Georgia Tech ,
Organizer:

In this talk I am going to present a way to study
numerically the complex domains of invariant Tori for the dissipative standar map. The numerical approach is based on a Nash Moser method. This is work in
progress jointly with R. Calleja.

Friday, November 4, 2016 - 15:05 ,
Location: Skiles 170 ,
Adrián P. Bustamante ,
Georgia Tech ,
Organizer:

In the first part of the talks we are going to present a way to study
numerically the complex domains of invariant Tori for the standar map.
The numerical method is based on Padé approximants. For this part we are
going to follow the work of C. Falcolini and R. de la LLave.In the
second part we are going to present how the numerical method, developed
earlier, can be used to study the complex domains of analyticity of
invariant KAM Tori for the dissipative standar map. This part is work in
progress jointly with R. Calleja (continuation of last talk).

Friday, October 28, 2016 - 15:05 ,
Location: Skiles 170 ,
Adrián P. Bustamante ,
Georgia Tech ,
Organizer:

In the first part of the talk(s) we are going to present a way to study
numerically the complex domains of invariant Tori for the standar map.
The numerical method is based on Padé approximants. For this part we are
going to follow the work of C. Falcolini and R. de la LLave.In the
second part we are going to present how the numerical method, developed
earlier, can be used to study the complex domains of analyticity of
invariant KAM Tori for the dissipative standar map. This part is work in
progress jointly with R. Calleja (continuation of last talk).

Friday, October 14, 2016 - 15:05 ,
Location: Skiles 170 ,
Adrián P. Bustamante ,
Georgia Tech ,
Organizer:

In the first part of the talk(s) we are going to present a way to study numerically the complex domains of invariant Tori for the standar map. The numerical method is based on Padé approximants. For this part we are going to follow the work of C. Falcolini and R. de la LLave.In the second part we are going to present how the numerical method, developed earlier, can be used to study the complex domains of analyticity of invariant KAM Tori for the dissipative standar map. This part is work in progress jointly with R. Calleja.

Friday, October 7, 2016 - 15:05 ,
Location: Skiles 170 ,
Livia Corsi ,
Georgia Tech ,
Organizer:

The aim of this talk is to
give a general overview of KAM theory, starting from its early stages
untill the modern era, including infinite dimensional cases. I'll try to
present the main ideas with as little technicalities as possible, and
if I have time I'll
also discuss some open problems in the field.

Thursday, April 14, 2016 - 15:05 ,
Location: Skiles 170 ,
Jiayin Jin ,
Georgia Tech ,
Organizer: Lei Zhang

In this talk, I will state the main results of center manifold theory for finite dimensional systems and give some simple examples to illustrate their applications. This is based on the book “Applications of Center Manifold Theory” by J. Carr.

Friday, April 1, 2016 - 13:05 ,
Location: Skiles 170 ,
Longmei Shu ,
Georgia Tech ,
Organizer: Lei Zhang

Isospectral Reduction reduces a higher dimension matrix to a lower dimension one while preserving the eigenvalues. This goal is achieved by allowing rational functions of lambda to be the entries of the reduced matrix. It has been shown that isospectral reduction also preserves the eigenvectors. Here we will discuss the conditions under which the generalized eigenvectors also get preserved. We will discuss some sufficient conditions and the reconstruction of the original network.

Friday, March 18, 2016 - 13:05 ,
Location: Skiles 170 ,
Hongyu Cheng ,
Georgia Tech ,
Organizer: Lei Zhang

We present some basic results from the theory of stochastic processes and investigate the properties of some standard continuous-time stochastic processes. Firstly, we give the deﬁnition of a stochastic process. Secondly, we introduce Brownian motion and study some of its properties. Thirdly, we give some classical examples of stochastic processes in continuous time and at last prove some famous theorems.