USA MathStat Graduate Student Seminar

Date	Speaker	Talk
Current Talks:
Friday, September 8, 2006	Norman Dean	Investigating the infinitude of Primes Abstract: Ever since the days of antiquity with Euclid, Mathematicians have been attracted to prime numbers. While hard to imagine, there are numbers billions of digits long which are not divisible by any number other than 1. In this talk, I will discuss various proofs that have been given to show that there must exist an infinite number of primes. The proofs are varied, ranging from number theoretic to ideas involving analysis, and I will give a breif historical background of each proof.
Friday, September 15, 2006	Kensaku Matsumura	Optimal block designs with minimal number of observations Abstract: Optimal block designs as per the D- and the E-criteria are identified in the class of connected block designs, when the number of experimental units is minimal.
Friday, September 22, 2006	Christopher Ogden	Determining the Maximum Rate of Transmission Abstract: Suppose we want to transmit messages across a channel where some symbols may be distorted to a receiver. We want to determine the maximum rate of transmission such that the receiver may recover the original message without errors. In this seminar session we will present Claude Shannon's 1956 solution to this problem utilizing confusion graphs of an arbitrary number of cycles. We will focus specifically upon utilizing his fundamental definition of the zero-error capacity to determine the upper and lower bounds for the maximum possible transmission rate across a channel without error with confusion graphs of five cycles or less. We shall also introduce László Lovász's umbrella and its refinement of the upper limit Shannon determined for the zero-error capacity of his C5 confusion graph.
Friday September 15th, 2006	Scott Brown	TITLE GOES HERE!!!! Abstract: ABSTRACT GOES HERE!!!
Friday, October 20, 2006	Vijay Kumar	Breaking Al Qaeda Cells: A Mathematical Analysis of Counterterrorism Operations Abstract: How can we tell if an Al Qaeda cell has been broken? That enough members have been captured or killed so that there is a high likelihood they will be unable to carry out a new attack, and military resources can be redirected away from them and toward more immediate threats? This article uses order theory to quantify the degree to which a terrorist network is still able to function. This tool will help law enforcement know when a battle against Al Qaeda has been won, thus saving the public's money without unduly risking the public's safety
Friday November 3, 2006	Jeannette Lymon	Representing Numbers as Sums of Two Squares. Abstract: "Which numbers can be written as the sum of two squares?" is a question as old as number theory with a solution that is considered classic in the field of number theory and proven throughout history by mathematicians including Pierre de Fermat, Axel Thue, and more recently Roger Heath-Brown. In this talk we will look at some of Fermat's work with prime numbers, Thue's proof with the "pigeonhole principle", and Heath-Brown's proof with three linear involutions to answer this question.

Date

Speaker

Talk

Current Talks:

Friday,
September 8, 2006

Norman Dean

Investigating the infinitude of Primes

Abstract: Ever since the days of antiquity with Euclid, Mathematicians have been attracted to prime numbers. While hard to imagine, there are numbers billions of digits long which are not divisible by any number other than 1. In this talk, I will discuss various proofs that have been given to show that there must exist an infinite number of primes. The proofs are varied, ranging from number theoretic to ideas involving analysis, and I will give a breif historical background of each proof.

Friday,
September 15, 2006

Kensaku Matsumura

Optimal block designs with minimal number of observations

Abstract: Optimal block designs as per the D- and the E-criteria are identified in the class of connected block designs, when the number of experimental units is minimal.

Friday,
September 22, 2006

Christopher Ogden

Determining the Maximum Rate of Transmission

Abstract: Suppose we want to transmit messages across a channel where some symbols may be distorted to a receiver. We want to determine the maximum rate of transmission such that the receiver may recover the original message without errors. In this seminar session we will present Claude Shannon's 1956 solution to this problem utilizing confusion graphs of an arbitrary number of cycles. We will focus specifically upon utilizing his fundamental definition of the zero-error capacity to determine the upper and lower bounds for the maximum possible transmission rate across a channel without error with confusion graphs of five cycles or less. We shall also introduce László Lovász's umbrella and its refinement of the upper limit Shannon determined for the zero-error capacity of his C5 confusion graph.

Friday
September 15th, 2006

Scott Brown

TITLE GOES HERE!!!!

Abstract: ABSTRACT GOES HERE!!!

Friday,
October 20, 2006

Vijay Kumar

Breaking Al Qaeda Cells: A Mathematical Analysis of Counterterrorism Operations

Abstract: How can we tell if an Al Qaeda cell has been broken? That enough members have been captured or killed so that there is a high likelihood they will be unable to carry out a new attack, and military resources can be redirected away from them and toward more immediate threats? This article uses order theory to quantify the degree to which a terrorist network is still able to function. This tool will help law enforcement know when a battle against Al Qaeda has been won, thus saving the public's money without unduly risking the public's safety

Friday
November 3, 2006

Jeannette Lymon

Representing Numbers as Sums of Two Squares.

Abstract: "Which numbers can be written as the sum of two squares?" is a question as old as number theory with a solution that is considered classic in the field of number theory and proven throughout history by mathematicians including Pierre de Fermat, Axel Thue, and more recently Roger Heath-Brown. In this talk we will look at some of Fermat's work with prime numbers, Thue's proof with the "pigeonhole principle", and Heath-Brown's proof with three linear involutions to answer this question.

USA Graduate Student Seminar

Fall 2006

Current Talks: