Spring 2014 Colloquia
New Problems in Matrix Theory
Ulrica Wilson, Morehouse College/ICERM
Tuesday, February 18 2:30 PM Q207
Refreshments 2 PM Building D Second Floor
An eventual property of a matrix M is a property that holds for all powers M^k, for some positive integer k. Eventually positive and eventually nonnegative matrices have been studied extensively since their introduction by Friedland in 1978. I will introduce some eventual properties of matrices and student projects that have come from this work. I will also describe an annual summer workshop for faculty at primarily undergraduate institutions jointly sponsored by the American Institute for Mathematics and the Institute for Computational and Experimental Research in Mathematics; and the EDGE Program for women entering PhD programs in mathematics.
Fall 2013 Colloquia
Albert Bush, Georgia Institute of Technology
Tuesday, October 22 3 PM Q207
Refreshments 2:30 PM Building D Second Floor
Erdos and Szemeredi conjectured that if one has a set of n integers, one must have either the sumset or product set be of nearly maximal size, n^(2-epsilon). In this talk, I will introduce the sum-product problem, show previous, beautiful geometric proofs by Solymosi and Elekes, and discuss some recent progress by myself and some collaborators.
Periods of sequences given by linear
recurrence relations mod p
Alan Koch, Agnes Scott College
Tuesday, September 17 3 PM Q207
Reception and snacks at 2:30pm on 2nd floor of Building D
Let p>2 be prime. Any integer sequence which satisfies a linear recurrence relation, for example the Fibonacci sequence, becomes periodic when reduced mod p. If w is the order of the recurrence relation then the period length of the sequence is bounded by pw-1. The length of the period also depends on the integer coefficients of the recurrence relation and the initial conditions for the sequence. Using linear algebra and some number theory we will determine which positive integers arise as period lengths for some sequence. In the case where w=2 we will give a formula for the probability that randomly chosen integer coefficients give a period length of p2-1.
Spring 2013 Colloquia
Symmetry Groups and Temari Balls Plus
Carolyn Yackel, Mercer University
Tuesday, March 26 4 PM Q207
Refreshments 3:30 PM Building D Second Floor
This talk will begin with a broad introduction to the field of mathematical fiber arts. The talk will then focus on presenting the 14 finite spherical symmetry groups and will show that they can be manufactured via the Japanese craft of temari (embroidered thread balls). Time permitting, the conclusion of the talk will move to a discussion of other interesting temari problems.
Give Me a Place To Stand, and I Will Make You Pi
Thursday, March 14, 3:14 PM Q 202
In Celebration of Pi Day
Professor Steven Edwards
We explore the life, times and achievements of Archimedes, the greatest engineer and mathematician of antiquity. Archimedes was the first to give a method that could be used to calculate pi to any degree of accuracy. In this talk we will give an introduction to some of Archimedes’ most interesting accomplishments, including his visionary method for calculating pi .
Mariana Montiel, Georgia State U.
Mon. Feb. 25th talk at 4pm in Q206
Meet the speaker: (coffee & cookies) 3:30pm 2nd floor D
Mathematical Music Theory: Some Selected Topics from a Research Field with Roots in the Origin of Modern Science.
Abstract: In the first part of this talk we will give an overview of some historical antecedents of modern Mathematical Music Theory, and how the study of musical objects has contributed to the advancement of scientific knowledge. We will also give a brief description of how certain notions and structures that this field has produced, such as maximal evenness and Vuza tiling (rhythmic) canons have led to the solution of open problems in Mathematics, as well as to applications in other sciences, such as Physics. In the second part of the talk, we will learn to identify well-formed scales by the symmetry condition, understand the duality relation (Sturmian involution) as it applies to the six authentic modes, and get a notion of the mathematical motivation behind the development of the software Rubato composer. whose Forms and Denotators provide a means for implementing an important part of Computational Category Theory. If time permits, we will describe the notions behind Euclidean Rhythms.
Fall 2012 Colloquia
Can Mathematics Heal All Wounds?
Richard Schugart, Western Kentucky University
Tuesday, November 27 3:00 PM Q 108
Refreshments at 2:30 2nd floor of the Mathematics Building (D)
In this talk, I will begin by providing background on the wound-healing process, the importance of oxygen in the wound-healing process, and methods for treatment with oxygen therapy. A mathematical model using differential equations will be presented for the treatment of a bacterial infection in a wound using oxygen therapy. Analysis of a sub-model (i.e., with two equations) and simulation results will be presented, with an emphasis on research results produced by undergraduate students. A modification to the model for the treatment of a chronic wound using optimal control theory will also be presented. Previous work will also be highlighted and briefly discussed.
How to Tame a Dragon
Scott M. Bailey, Clayton State University
Monday, October 29 4:15 PM Q 109
Paul Levy introduced the "Levy Dragon" fractal in 1938. Although it has become a well-known and well-studied example in the field of fractals, the question of "What does the Levy Dragon look like?" has never been answered. In this talk, we will answer this question by journeying deep inside Paul Levy's dragon, and find that it is very tame after all.
Euclid and Dehn in the Operating Room
Margaret Symington, Mercer University
Tues. Sept. 25 4pm Q 108
Refreshments at 3:30 2nd floor of the Mathematics Building (D)
In this talk I will describe how a quest for the mathematics behind a
surgical improvement led to some interesting Euclidean geometry and
highlighted a little known kinship between dermatologists and geometric
topologists. Along the way I will share some topological gems and pose a set of geometry questions that anyone can work on.