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Mathematics Department Events

Spring 2015 Colloquia

Translation Lengths of Point-Pushing Pseudo-Anosov Maps of Riemann Surfaces. Chaohui Zhang of Morehouse College

Thursday February 19, 2:30pm in A 215 (Student Center)

Abstract:  Let S be a hyperbolic Riemann surface of genus p > 1, which has no free boundary curve and contains only one puncture x. Let C(S) denote the curve complex of S, which is equipped with a path metric dC. Let C0(S) denote the set of vertices of C(S). Masur-Minsky showed that there exists a constant c > 0 such that for any pseudo-Anosov map f : S →S, any integer n and u in C0(S), we have dC(u, fn(u)) > c|n|.

In this presentation, we first prove that for any multi twist fdC(u, fm(u)) remains bounded. Then we consider the subgroup F of the mapping class group Mod(S) which consists of elements isotopic to the identity on S U {x}. We show that for any pseudo-Anosov element f in FdC(u, fm(u)) ≥ m for m = 1, 2, ..., 7;  and dC(u, fm(u)) (2m + 5)/3 for m > 7. It follows that the action of any pseudo-Anosov element f in F on C(S) is hyperbolic (in the sense of Gromov). Furthermore, we obtain a positive lower bound on the translation length for the action of f on C(S).



Fall 2014 Colloquia

Computational Graph Theory. Brian Patterson, Oglethorpe University

Thursday October 23, 2:30pm in A 216 (Student Center)

Abstract: Dr. Patterson will present two areas of graph theory in mathematics of interest to computer scientists: the optimal weighted Hamiltonian cycle problem (also called traveling salesperson) and the graph coloring problem.  The traveling salesperson problem is sometimes used in Oglethorpe’s core mathematics class to explain an intractable but useful mathematical problem that computer science provides approximate solutions for.  Two algorithms will be presented.  The graph coloring problem is a challenging and ongoing area of mathematical research with many applications to scheduling problems.  It is presented briefly in the Oglethorpe core mathematics course but explored more thoroughly in the upper-level graph theory class and independent study.  Depth-first and genetic algorithms approaches will be presented.



How small is too small? Modeling the effects of habitat fragmentation via reaction diffusion equations. Jerome Goddard II, Auburn University

Monday September 22, 2:30pm  Ballroom B (Student Center)

Abstract: Habitat fragmentation occurs when an organism’s preferred habitat is divided or broken into smaller fragments (called patches) and can be caused by natural events, such as geological processes, or human activity, such as land conversion. Habitat fragmentation is often cited as a contributor to animal species becoming threatened or endangered. Two important aspects of habitat fragmentation are the size of fragmented patches of preferred habitat and the inferior habitat surrounding the patches, called the matrix. Ecological field studies have indicated that an organism’s survival in a patch is often linked to both the size of the patch and the quality of its surrounding matrix. In this talk, we will focus on modeling the effects of habitat fragmentation via the reaction diffusion framework. The reaction diffusion framework has been extensively employed in population dynamics providing important biological insight into the patch-level consequences of various assumptions made on individual behavior in ecological systems. Such models have seen enormous success both in their empirical validation with actual spatio-temporal distribution data and their ability to yield general conclusions about an eco-system based on the analytical results of these theoretical models. First, we will introduce the reaction diffusion framework and a specific reaction diffusion model with logistic growth and Robin boundary condition (which will model the negative effects of the patch matrix). Second, we will use mathematics to explore the dynamics of the model via the well-known quadrature method and ultimately obtain a causal relationship between the size of the patch and the quality of the matrix versus the maximum population density sustainable by that patch. This important example regarding habitat fragmentation will hopefully serve to illustrate the usefulness of mathematical models in helping to understand complex biological relationships.


Spring 2014 Colloquia


Wavelets, the Molecules and Atoms of the Mathematical Universe
Josip Derado, Kennesaw State University

TuesdayMarch 25  2:30pm  Q207

Wavelets are the building blocks of a mathematical universe. Specifically they are an orthonormal basis for the function spaces. In this talk we will present an introduction into wavelet theory. We will start with Haar wavelets, and we will see how their structure is generalized by Yves Meyer and Stephan Mallat. We will then see how to construct Daubechies wavelets. At the end we will talk about some open problems in the wavelet theory.


The Life of Pi: On the Life and Contributions of Ramanujan        Zhu Cao, SPSU

Q202, 3:14 PM  Piday March 14

Although he died at the age of 32, legendary Indian mathematician Srinivasa Ramanujan independently established nearly 3900 results (mostly identities and equations) that are recorded in his three notebooks and his "lost" notebook. During his short lifetime, he made remarkable contributions to number theory, combinatorics, and analysis, among them fascinating formulas that can be used to calculate digits of pi in unusual ways. In this talk, I’ll give an introduction of some formulas for pi and the life of Ramanujan.


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


Sum-Product Inequalities
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
ursday, 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.