Seminars and Colloquia by Series

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 Huynh – School 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 Ni – School 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 Zhang – School 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 Yin – School 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).

Baby Representation Theory of Finite Groups

Series
SIAM Student Seminar
Time
Friday, February 13, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Yi Huang – School of Mathematics, Georgia Tech
Let V be a vector space over the field C of complex numbers and let GL(V) be the group of isomorphisms of onto itself. Suppose G is a finite group. A linear representation of G in V is a homomorphism from the group G into the group GL(V). In this talk, I will give a brief introduction to some basic theorems about linear representations of finite groups with concentration on the decomposition of a representation into irreducible sub-representations, and the definition and some nice properties of the character. At the end of the talk, I will re-prove the Burnside lemma in the group theory from the representation theory approach. Since I began learning the topic only very recently, hence an absolute novice myself, I invite all of you to the talk to help me learn the knowledge through presenting it to others. If you are familiar with the topic and want to learn something new, my talk can easily be a disappointment.

Simple Proof of the Law of Iterated Logarithm in Probability

Series
SIAM Student Seminar
Time
Friday, January 30, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Jinyong Ma – School of Mathematics, Georgia Tech
I plan to give a simple proof of the law of iterated logarithm in probability, which is a famous conclusion relative to strong law of large number, and in the proof I will cover the definition of some important notations in probability such as Moment generating function and large deviations, the proof is basically from Billingsley's book and I made some.

Some interesting examples in the conditional expectation and martingale

Series
SIAM Student Seminar
Time
Friday, January 23, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Linwei Xin – School of Mathematics, Georgia Tech
In this talk, I will focus on some interesting examples in the conditional expectation and martingale, for example, gambling system "Martingale", Polya's urn scheme, Galton-Watson process, Wright-Fisher model of population genetics. I will skip the theorems and properties. Definitions to support the examples will be introduced. The talk will not assume a lot of probability, just some basic measure theory.

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