Seminars and Colloquia by Series

Frames and integral operators

Series
SIAM Student Seminar
Time
Friday, October 2, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Shannon BishopGeorgia Tech
I will describe some interesting properties of frames and Gabor frames in particular. Then we will examine how frames may lead to interesting decompositions of integral operators. In particular, I will share some theorems for pseudodifferential operators and Fourier integral operators arising from Gabor frames.

Dynamics of Functions with an Eventual Negative Schwarzian Derivative

Series
SIAM Student Seminar
Time
Friday, September 25, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Benjamin WebbSchool of Mathematics, Georgia Tech
In the study of one dimensional dynamical systems one often assumes that the functions involved have a negative Schwarzian derivative. In this talk we consider a generalization of this condition. Specifically, we consider the interval functions of a real variable having some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functions. The introduction of this class was motivated by some maps arising in neuroscience

Viscosity and Principal-Agnet Problem

Series
SIAM Student Seminar
Time
Friday, September 11, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ruoting GongGeorgia Tech
We develop a stochastic control system from a continuous-time Principal-Agent model in which both the principal and the agent have imperfect information and different beliefs about the project. We attempt to optimize the agent’s utility function under the agent’s belief. Via the corresponding Hamilton-Jacobi-Bellman equation we prove that the value function is jointly continuous and satisfies the Dynamic Programming Principle. These properties directly lead to the conclusion that the value function is a viscosity solution of the HJB equation. Uniqueness is then also established.

Linear algebra method in combinatorics

Series
SIAM Student Seminar
Time
Friday, April 10, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Tianjun YeSchool of Mathematics, Georgia Tech
Linear algebra method is a very useful method in combinatorics. Lovas Theorem (a very deep theorem about perfect graph) is proved by using this way. The idea is, if we want to come up with an upper bound on the size of a set of objects, associate them with elements in a vector space V of relatively low dimension, and show that these elements are linearly independent. Then we cannot have more objects in our set than the dimension of V. We will show we can use this way to solve some combinatorics problem, such as odd town problem and two-distance sets problem.

Small random perturbation of ODE around hyperbolic points

Series
SIAM Student Seminar
Time
Friday, April 3, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Sergio AlmadaSchool of Mathematics, Georgia Tech
Suppose b is a vector field in R^n such that b(0) = 0. Let A = Jb(0) the Jacobian matrix of b at 0. Suppose that A has no zero eigenvalues, at least one positive and at least one negative eigenvalue. I will study the behavior of the stochastic differential equation dX_\epsilon = b(X_\epsilon) + \epsilon dW as \epsilon goes to 0. I will illustrate the techniques done to deal with this kind of equation and make remarks on how the solution behaves as compared to the deterministic case.

Longest Increasing Subsequence for Finite Alphabets

Series
SIAM Student Seminar
Time
Friday, March 27, 2009 - 12:30 for 2 hours
Location
Skiles 255
Speaker
Huy HuynhSchool of Mathematics, Georgia Tech
This is due to the paper of Dr. Christian Houdre and Trevis Litherland. Let X_1, X_2,..., X_n be a sequence of iid random variables drawn uniformly from a finite ordered alphabets (a_1,...,a_m) where a_1 < a_2 < ...< a_m. Let LI_n be the length of the longest increasing subsequence of X_1,X_2,...,X_n. We'll express the limit distribution of LI_n as functionals of (m-1)-dimensional Brownian motion. This is an elementary case taken from this paper.

An introduction to mathematical learning theory

Series
SIAM Student Seminar
Time
Friday, March 6, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Kai NiSchool of Mathematics, Georgia Tech
In this talk, I will briefly introduce some basics of mathematical learning theory. Two basic methods named perceptron algorithm and support vector machine will be explained for the separable classification case. Also, the subgaussian random variable and Hoeffding inequality will be mentioned in order to provide the upper bound for the deviation of the empirical risk. If time permits, the Vapnik combinatorics will be involved for shaper bounds of this deviation.

Fredholm operators

Series
SIAM Student Seminar
Time
Friday, February 27, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Weizhe ZhangSchool of Mathematics, Georgia Tech
This talk will follow Peter Lax on the linear algebraic fact of the index of Fredholm operators such as the product formula and stability, all of which are totally elementary.

Introduction to basic governing equations of fluid dynamics

Series
SIAM Student Seminar
Time
Friday, February 20, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Ke YinSchool of Mathematics, Georgia Tech
In this introductory talk, I am going to derive the basic governing equations of fluid dynamics. Our assumption are the three physical principles: the conservation of mass, Newton's second law, and the conservation of energy. The main object is to present Euler equations (which characterize inviscid flow) and Navier-Stokes equations (which characterize viscid flow).

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