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Friday, October 19, 2018 - 15:05 ,
Location: Skiles 156 ,
Jiaqi Yang ,
GT Math ,
Organizer: Jiaqi Yang

We show that, if the linearization of a map at a fixed point leaves invariant a spectral subspace, and some non-resonance conditions are satisfied. Then the map leaves invariant a smooth (as smooth as the map) manifold, which is unique among C^L invariant manifolds. Here, L only depends on the spectrum of the linearization. This is based on a work of Prof. Rafael de la Llave.

Friday, October 5, 2018 - 15:05 ,
Location: Skiles 156 ,
Adrian P. Bustamante ,
Georgia Tech ,
Organizer: Adrian Perez Bustamante

In this talk I will present a proof of a generalization of a theorem by
Siegel, about the existence of an analytic conjugation between an
analytic map, $f(z)=\Lambda z +\hat{f}(z)$, and a linear map, $\Lambda
z$, in $\mathbb{C}^n$. This proof illustrates a standar technique used
to deal with small divisors problems. I will be following the work of E.
Zehnder. This is a continuation of last week talk.

Friday, September 28, 2018 - 15:05 ,
Location: Skiles 156 ,
Adrian P. Bustamante ,
Georgia Tech ,
Organizer: Adrian Perez Bustamante
In this talk I will present a proof of a generalization of a theorem by
Siegel, about the existence of an analytic conjugation between an
analytic map, $f(z)=\Lambda z +\hat{f}(z)$, and a linear map, $\Lambda
z$, in $\mathbb{C}^n$. This proof illustrates a standar technique used
to deal with small divisors problems. I will be following the work of E.
Zehnder. This is a continuation of last week talk.

Friday, September 21, 2018 - 15:05 ,
Location: Skiles 156 ,
Adrian P. Bustamante ,
Georgia Tech ,
Organizer: Adrian Perez Bustamante

In this talk I will present a proof of a generalization of a theorem by Siegel, about the existence of an analytic conjugation between an analytic map, $f(z)=\Lambda z +\hat{f}(z)$, and a linear map, $\Lambda z$, in $\mathbb{C}^n$. This proof illustrates a standar technique used to deal with small divisors problems. I will be following the work of E. Zehnder.

Friday, September 7, 2018 - 15:05 ,
Location: Skiles 156 ,
Adrian P. Bustamante ,
Georgia Tech ,
Organizer: Adrian Perez Bustamante

In this talk we will discuss the paper of McGehee titled "The stable manifold theorem via an isolating block," in which a proof of the theorem is made using only elementary topology of Euclidean spaces and elementary linear algebra.

Wednesday, May 30, 2018 - 14:00 ,
Location: Skiles 006 ,
Tongzhou Chen ,
GT Math ,
Organizer: Jiaqi Yang

We model and analyze the dynamics of religious group membership
and size. A groups is distinguished by its strictness, which determines
how much time group members are expected to spend contributing to the
group. Individuals differ in their rate of return for time spent outside
of their religious group. We construct a utility function that individ-
uals attempt to maximize, then find a Nash Equilibrium for religious
group participation with a heterogeneous population. We then model
dynamics of group size by including birth, death, and switching of
individuals between groups. Group switching depends on the strictness
preferences of individuals and their probability of encountering members
of other groups.

Friday, April 27, 2018 - 15:05 ,
Location: Skiles 271 ,
Bhanu Kumar ,
GTMath ,
Organizer: Jiaqi Yang

This talk follows Chapter 4 of the well known text by Guckenheimer and Holmes. It is intended to present the theorems on averaging for systems with periodic perturbation, but slow evolution of the solution. Also, a discussion of Melnikov’s method for finding persistence of homoclinic orbits and periodic orbits will also be given. Time permitting, an application to the circular restricted three body problem may also be included.

Friday, April 20, 2018 - 15:05 ,
Location: Skiles 271 ,
Prof. Rafael de la Llave ,
GT Math ,
Organizer: Jiaqi Yang

A well known paper of H. Federer on Flat chains contains a remarkable example attributed to F. Almgren. We intend to give a geometric exposition of the example and explain its relevance in the global theory of geodesic flows and some global problems such as homogenization in quasi-periodic media. This is part of an expository paper with X. Su.

Friday, April 20, 2018 - 15:05 ,
Location: Skiles 271 ,
Prof. Rafael de la Llave ,
GT Math ,
Organizer: Jiaqi Yang
A well known paper of H. Federer on Flat chains contains a remarkable example attributed to F. Almgren. We intend to give a geometric exposition of the example and explain its relevance in the global theory of geodesic flows and some global problems such as homogenization in quasi-periodic media. This is part of an expository paper with X. Su.

Friday, March 16, 2018 - 15:05 ,
Location: Skiles 271 ,
Longmei Shu ,
GT Math ,
Organizer: Jiaqi Yang

Isospectral reductions decrease the dimension of the adjacency matrix
while keeping all the eigenvalues. This is achieved by using rational
functions in the entries of the reduced matrix. I will show how it's
done through an example. I will also discuss about the eigenvectors and
generalized eigenvectors before and after reductions.