Fall 2003 GSS Schedule

Organizers: Jason Howell and Mark Liu

Date Speaker Topic Abstract
August 25 Todd Michel ,
Timothy Flowers ,
Shannon Purvis ,
John Paul Roop 		Life in the Department of Mathematical Sciences In this talk, four graduate students with experience in the M.S. and Ph.D. programs in the department of Mathematical Sciences at Clemson will discuss some of their experiences at different levels and how they differed from their expectations. Todd Michel is a second-year master's student here in the department. Timothy Flowers recently completed the M.S. degree and has now entered the Ph.D. program. Shannon Purvis is a Ph.D. student who recently completed the qualifying examinations. John Paul Roop is also a doctoral student who is currently working on his dissertation.

The main purpose of this talk is to promote candid discussion among new and experienced graduate students about the realities of graduate school here.(slides)
September 1 Labor Day
September 10 Lara Diamond from the National Security Agency The NSA and SPORT The National Security Agency (NSA)'s Summer Program in Operations Research Technology (SPORT) is a paid summer internship where graduate students (as well as seniors who will attend graduate school the following fall semester) can apply skills learned in classes such as Operations Research, Industrial Engineering, Graph Theory, Stochastic Processes, and more, to real-world problems.

Lara Diamond, SPORT Director, will give an overview of the SPORT program, some projects worked on by SPORT participants in previous years, and will be happy to take questions from anyone who may be interested. She is also a former two-time participant in the SPORT program.

Dr. Shier has several brochures for those who would like to learn more before the 10th.
September 15 Alan Thomas Random Walks on Sierpinski Lattices Probability is FUN! Fractals are FUN! What happens when you put the two together? 2FUN? FUN^2 ? In this talk, we will develop the notion of a simple random walk. We will then introduce the fractal like Sierpinski Triangle as the limit of Sierpinski Lattices. After this, we will use a symmetry argument to extended our notion of a random walk to the self similar Sierpinski Lattices. Finally we will consider the limit of these walks as we refine our lattices. I hope that this talk will be accessible to undergraduates but still interesting to professors. {Fun} for this talk is guaranteed to be of at least Hausdorff dimension 2.
September 22 Thomas McCoy Misrepresenting Control Chart Data - A Statistical Quality Control (SQC) Case Study In this talk we will examine a specific instance of a misapplication of a statistical tool heavily used in industry called the control chart. The control chart is a method designed to monitor process characteristics such as sample averages or proportions via graphical techniques so that even personnel without formal statistical training can make use of them. Control charts are typically implemented along side another important quality control tool called process capability. We will examine a specific instance where improper procedures were used in the formulation of the control chart, and discuss ramifications of such actions on the validity of process capability, all within the framework of the QS-9000 quality system. This talk will be accessible to those without quality engineering or statistics backgrounds.
September 29 Tim Flowers Plane Partitions and Alternating Sign Matrices Twenty years ago, three mathematicians made a conjecture for counting the number of n x n alternating sign matrices. Then they discovered that someone else already had seen those same numbers - but he had been counting a certain type of restricted plane partition. In the years since, many proofs and results have been found in each of these seemingly unconnected fields. The first goal of this talk will be to give a basic overview of the alternating sign matrix (ASM) and plane partitions, taking time to examine the relationship between plane partitions and the integer partition (which is studied much more frequently). Next, we will follow the story of the conjectures, theorems, and proofs which has emerged in recent years, including the surprising twist in 1996. Finally, we will look briefly at some results relating to divisibility patterns in counting ASM's.
October 6 Robert Beeler Pascal's Wager - The Search for God in a Mathematical World In 1656, Blaise Pascal began writing his most famous philosophical work, the Pensées. Included in this is the following arguement for the belief in God: "If God does not exist, one will lose nothing by believing in him, while if he does exist, one will lose everything by not believing." This arguement, known as Pascal's wager, uses mathematical probability, in particular the expected value of a random variable, to support his belief in God. In this talk, we will examine the short comings of Pascal's wager, as well as posssible ways to rectify. Other mathematical arguements for the existence of God may be discussed as time permits.

"...we are compelled to gamble..." - Blaise Pascal, 1656
October 13 John Paul Roop Numerical Approximation of Fractional Advection-Diffusion Equations In this talk, we introduce the fractional advection-dispersion equation, and discuss how it generalizes the ordinary advection-dispersion equation to include a dispersive term involving a fractional differential operator. We then present analysis behind a Galerkin formulation of time independent and time dependent fractional advection-dispersion equation. Existence and uniqueness results are presented for the time independent and time dependent problems, as well as error estimates. Numerical results are included which confirm the theoretical estimates.
October 20 Fall Break
October 27 Professor Gary L. Mullen A Candidate for the Next Fermat Problem Now that Fermat's Last Theorem has been shown to be true, many mathematicians have discussed their favorite problem which might be put forward as a candidate for the Next Fermat Problem. In this talk we will discuss a number of problems which have been proposed for this very distinguished honor. I will also discuss my favorite candidate which involves latin squares. This talk will be of a very elementary nature and so both undergraduate as well as graduate students are encouraged to attend.

Professor Mullen is a Professor of Mathematics and just finished his second three year term as a Chair of the Mathematics Department at The Pennsylvania State University. His research interests are in number theory, in particular finite fields, and combinatorics, along with applications. He has published over 100 research papers, and is the Editor-in-Chief of the international journal Finite Fields and Their Applications published by Elsevier.
November 3 Olena Gavriliouk Hubs, Aggregation, and Their Combination In 1986 the Hub Location problem was introduced to the research community. Because of its important applications, it quickly became very popular. The difficulty of the problem and its relative novelty open many opportunities for research. We will talk about hub location problems and mention some of the open areas of research. Also we introduce another concept that recently has been getting some attention in Location Theory---aggregation (also a topic with many open problems). We explore a way aggregation can be applied in hub location models.

We hope that this talk will benefit those interested in Integer Programming and Location Theory and the ``undecided," who are looking for thesis/project topics.
November 10 Jang-Woo Park Algebraic Properties of the Digraph Generated by the Iteration of the Quadratic Mapping x -> x^2 -2 in GF(p) The digraph generated by iterating the quadratic mapping x -> x^2 - 2 in GF(p) shows a similar structure with one generated by the square mapping x -> x^2 in GF(p). We explain this by defining new groups with elements of GF(p^2)^2 and a squaring mapping in GF(p^2)^2 which corresponds to the quadratic mapping x^2 - 2 in GF(p). As a result, elements in GF(p) can be considered as projected images of elements in GF(p^2)^2 by a simple projection mapping and properties of the original digraph reflect properties of the squaring mapping on the new groups.