Seminars and Colloquia by Series

Tuesday, November 19, 2013 - 16:05 , Location: Skiles 005 , Mikel J. de Viana , Georgia Tech , Organizer:
We conclude the proof of the linearization theorem for fibered holomorphic maps by showing that the iteration scheme we proposed converges. If time allows, we will comment on related work by Mario Ponce and generalizations of the theorem for fibered holomorphic maps in higher dimensions. 
Tuesday, November 12, 2013 - 15:00 , Location: Skiles 06 , Mikel J. de Viana , Georgia Tech , Organizer: Rafael de la Llave
Given f: \C \times T^1 to itself, an analytic perturbation of a fibered rotation map ,   we will present two proofs of existence of an analytic conjugation of f to the fibered rotation , on a neighborhood of {0} \times T^1. This talk will be self- contained except for some usual "tricks" from KAM theory and which will be explained better in another talk. In the talk we will discuss carefully the number theoretic conditions on the fibered rotation needed to obtain the theorem.
Tuesday, October 29, 2013 - 15:05 , Location: Skiles 06 , Chongchun Zeng , Georgia Tech , Organizer: Rafael de la Llave
Incompressible Euler equation is known to be the geodesic flow on the manifold of volume preserving maps. In this informal seminar, we will discuss how this geometric and Lagrangian point of view may help us understand certain analytic and dynamic aspects of this PDE.
Monday, October 21, 2013 - 15:05 , Location: Skiles 006 , Chongchun Zeng , Georgia Tech , Organizer: Rafael de la Llave
Incompressible Euler equation is known to be the geodesic flow on the manifold of volume preserving maps. In this informal seminar, we will discuss how this geometric and Lagrangian point of view may help us understand certain analytic and dynamic aspects of this PDE.
Wednesday, October 16, 2013 - 15:05 , Location: Skiles 006 , Chongchun Zeng , Georgia Tech , Organizer: Chongchun Zeng
Incompressible Euler equation is known to be the geodesic flow on the manifold of volume preserving maps. In this informal seminar, we will discuss how this geometric and Lagrangian point of view may help us understand certain analytic and dynamic aspects of this PDE.
Tuesday, October 8, 2013 - 16:05 , Location: skiles 006 , Mikel J. de Viana , Georgia Tech , Organizer:
Given f: \C \times T^1 to itself, an analytic perturbation of a fibered rotation map ,   we will present two proofs of existence of an analytic conjugation of f to the fibered rotation , on a neighborhood of {0} \times T^1. This talk will be self- contained except for some usual "tricks" from KAM theory and which will be explained better in another talk. In the talk we will discuss carefully the number theoretic conditions on the fibered rotation needed to obtain the theorem.
Tuesday, March 26, 2013 - 16:30 , Location: Skiles 006 , Xifeng Su , Academy of Mathematics and Systems Science, Chinese Academy of Sciences , billy3492@gmail.com , Organizer:
We consider the evolutionary first order nonlinear partial differential equations of the most general form \frac{\partial u}{\partial t} + H(x, u, d_x u)=0.By virtue of introducing a new type of solution semigroup, we  establish the weak KAM theorem for such partial differential equations, i.e. the existence of weak KAM solutions or viscosity solutions. Indeed, by employing dynamical approach for characteristics, we develop the theory of associated global viscosity solutions in general.  Moreover, the solution semigroup acting on any given continuous function will converge to a uniform limit as the time goes to infinity. As an application, we prove that such limit satisfies the  the associated stationary first order  partial differential equations:  H(x, u, d_x u)=0.
Tuesday, February 26, 2013 - 16:30 , Location: Skiles 06 , F. Fenton , Georgia Tech (Physics) , Organizer: Rafael de la Llave
The heart is an electro-mechanical system in which, under normal conditions, electrical waves propagate in a coordinated manner to initiate an efficient contraction. In pathologic states, propagation can destabilize and exhibit period-doubling bifurcations that can result in both quasiperiodic and spatiotemporally chaotic oscillations. In turn, these oscillations can lead to single or multiple rapidly rotating spiral or scroll waves that generate complex spatiotemporal patterns of activation that inhibit contraction and can be lethal if untreated. Despite much study, little is known about the actual mechanisms that initiate, perpetuate, and terminate reentrant waves in cardiac tissue. In this talk, I will discuss experimental and theoretical approaches to understanding the dynamics of cardiac arrhythmias. Then I will show how state-of-the-art voltage-sensitive fluorescent dyes can be used to image the electrical waves present in cardiac tissue, leading to new insights about their underlying dynamics. I will establish a relationship between the response of cardiac tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. I will discuss how in response to a pulsed electric field E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ?(E) and a characteristic time constant ? for tissue excitation that obeys a power law. These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. Therefore, rapid synchronization of cardiac tissue and termination of fibrillation can be achieved with a series of low-energy pulses. I will finish with results showing the efficacy and clinical application of this novel low energy mechanism in vitro and in vivo. e
Tuesday, January 29, 2013 - 16:30 , Location: Skiles 06 , Rafael de la Llave , Georgia Tech , Organizer: Rafael de la Llave
We will present the method of correctly aligned windows and show how it can lead to large scale motions when there are homoclinic orbits to a normally hyperbolic manifold.
Tuesday, November 20, 2012 - 16:30 , Location: Skiles 006 , Rafael de la Llave , Georgia Tech , Organizer: Rafael de la Llave
We will continue the presentation of some tools to obtain computer assisted proofs in dynamics using functional analysis methods. Joint work with D. Rana, R. Calleja.

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