Seminars and Colloquia by Series

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.
Friday, March 11, 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.
Friday, March 4, 2016 - 13:05 , 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, February 26, 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.
Friday, February 19, 2016 - 13:00 , Location: Skiles 170 , Lei Zhang , Georgia Inst. of Technology , Organizer: Rafael de la Llave
The Peierls barrier is an observable which  characterizes  whether the the set minimizers with a prescribed frequency  of a periodic variational problem form a continuum or have gaps. In solid state physics Peierls barrier characterizes whether  ground states with a fixed density are  pinned  or are  able to slide. The Peierls barrier is  a  microscopic explanation of static friction. Remarkably, in dynamical systems, Peierls barrier  appears also as  characterizing whether KAM circles break down into Cantor sets.  Hence, the Peierls barrier has been investigated both by physicists and by mathematicians using a variety of methods. We plan to cover the basic definitions of the variational models and some of the basic results obtainedfrom the 80's. Continuation of last week's seminar   
Friday, February 12, 2016 - 13:00 , Location: Skiles 170 , Lei Zhang , Georgia Tech , Organizer: Rafael de la Llave
The Peierls barrier is an observable which  characterizes  whether the the set minimizers with a prescribed frequency  of a periodic variational problem form a continuum or have gaps. In solid state physics Peierls barrier characterizes whether  ground states with a fixed density are  pinned  or are  able to slide. The Peierls barrier is  a  microscopic explanation of static friction. Remarkably, in dynamical systems, Peierls barrier  appears also as  characterizing whether KAM circles break down into Cantor sets.  Hence, the Peierls barrier has been investigated both by physicists and by mathematicians using a variety of methods. We plan to cover the basic definitions of the variational models and some of the basic results obtainedfrom the 80's.

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