Colloquium 2/15: Dr. Tracy Weyand on “The Spectra of the Magnetic Schrodinger Operator on Graphs”

On Monday at 3:30 PM in Math 357, Dr. Tracy Weyand of Baylor University will be talking about “The Spectra of the Magnetic Schrodinger Operator on Graphs.

Abstract: In the most general sense, a graph represents a relationship between a set of objects. Applications appear in chemistry, physics, engineering, computer science, and social science to name a few. In most applications, the relationship between objects (vertices) is represented by an operator that acts on functions whose domain is the graph. My research focuses on studying the spectra and corresponding eigenfunctions of such operators.

Throughout this talk, we will consider two types of graphs: discrete and metric. Eigenvalues of the magnetic Schrodinger operator on both types of graphs can be considered functions of the magnetic flux on the graph. Viewing the eigenvalues as functions, we have been able to determine their Morse index (a measure of stability). This result has led to progress on several other problems including the inverse problem (information the eigenvalues provide about the structure of a graph) and the location of Dirac cones (touching points) in the spectral bands (as well as properties of the corresponding eigenfunctions there).

(flyer in PDF form)

Colloquium 12/10: Dr. Seth Oppenheimer on “A Collection of Models and Applications”

On Thursday December 10th at 3:30 PM in Math 357, Dr. Seth Oppenheimer will be talking about “A Collection of Models and Applications.” This talk will be descriptive and nontechnical, accessible to undergraduates who understand a derivative as a rate of change. (Flyer in PDF form)

Abstract:Mathematics can be used to describe a wide variety of phenomena with great precision.  An applied mathematician, through discussion, careful listening, and a willingness to ask simple questions, can take the verbal description of what an investigator or experimentalist thinks is happening in his or her observations and build a clean mathematical model that is subject to analysis.  Such models sometimes lead to a quick rejection of the investigators theory.  Sometimes they lead to questions that require more experimental work and the model’s refining.  Often, interesting mathematical questions arise that require their own explorations.  Sometimes deep and difficult mathematics is needed and sometimes only a deep understanding of simple mathematics. The point is, mathematics can be a subtle probe in a variety of areas.  However, it is frequently the case that only someone coming out of deep engagement with mathematics can make full use of mathematics in a scientific setting.

In my career I have had the good fortune to work with excellent collaborators in both mathematics and in several areas of science and engineering.  This has allowed me to work on a variety of cool applications as well as giving me the tools to find some interesting problems independent of disciplinary investigators. Often this work has involved the creation of novel mathematical models and their analysis.  We will take a journey through nearly thirty years of fun applications that show the power of mathematics to illuminate problems in several areas and the realization via collaboration that the whole is often greater than the sum of the parts.

This talk will be descriptive and nontechnical, accessible to undergraduates who understand a derivative as a rate of change.

 

Colloquium 11/16: Dr. Robert Vallin on “Mathematics and Card Magic”

On Monday November 16th, at 3:30 PM in Math 357, Dr. Robert Vallin of Lamar University will be talking about “Mathematics and Card Magic.” This talk will be accessible for all students and Dr. Vallin is an excellent speaker. (flyer in PDF form)

Abstract: Recreational Mathematics is about doing mathematics for fun, rather than research. It covers many topics including games, puzzles, juggling, art, and more. It has had no greater champion than Martin Gardner, who wrote the Mathematical Games column for “Scientific American” for 25 years. In this talk we will look at several card tricks that are based on mathematics and were introduced to the world at large by Gardner, and show some of the workings behind them. We will further see how one particular trick relates to some known ideas and leads to developing new mathematics.

Colloquium 11/9: Dr. Nick Long on “Easy Unsolved Algebra Problems”

Our next colloquium will be on Monday November 9th at 3:30 PM in Math 357. Dr. Nick Long will be talking about “Easy Unsolved Algebra Problems.” This talk will be accessible and interesting for students with experience or interest in linear algebra.

Abstract:Dynamical systems is a branch of mathematics that uses many tools from many different areas of mathematics to help describe the behavior of changing systems. Symbolic Dynamics deals with the changes that can be described by infinite sequences of symbols. For example, the data on computers is stored and manipulated as a long sequences of zeros and ones but can exhibit interesting behaviors like chaos. We will look at some problems that can be stated in basic linear algebra terms, but the answers are still mostly or partially unknown. All that is needed to solve them is another good idea. (flyer in PDF form)

Colloquium 9/17: Dr. Mark Webb on “Edge Ideals”

On Monday September 21st at 3:30 PM in Math 357, Dr. Mark Webb will be giving our first colloquium of the semester on “Edge Ideals.” Be sure to invite any students who have an interest in algebra.

Abstract:

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How many distinct triangles can you find in the graph above? What about graphs that aren’t complete? One interesting solution involves associating the graph with a collection of polynomials – called the edge ideal. This association allows one to use algebra to study graphs. In this talk, we will present a hands-on approach to this field, using SAGE to compute examples and explore recent results and open problems in this area.

Colloquium 2/23: Marcus Webb on “The Freshman’s Dream”

On Monday, February 23rd at 3:30 PM in Math 357, Marcus Webb will talk about “The Freshman’s Dream.” Abstract: Let A be an m by n matrix with entries in some finite field – the integers modulo a prime p, for example. What happens to the kernel of A when we raise each entry to the p’th power? In this talk, we will answer this question and consider its generalization to matrices with entries in a commutative ring of prime characteristic. For such rings, every freshman’s dream is true: (a+b)p=ap+bp, and we will explore some of the remarkable consequences of this equality. (flyer in PDF form)

 

Colloquium 2/16: Dr. Jonathan Mitchell on “The Effect of a State-Dependent Delay on a Weakly-Damped Nonlinear Oscillator”

On Monday February 16th at 3:30 in Math 357, Dr. Jonathan Mitchell will be talking about “The Effect of a State-Dependent Delay on a Weakly-Damped Nonlinear Oscillator.” Abstract: We consider a weakly-damped nonlinear oscillator with state-dependent delay which has applications in models for lasers, epidemics, and micro-parasites. We begin by introducing a nonlinear oscillator stemming from the usual predator-prey system and analyzing the evolution of its energy. We will incorporate a constant time lag in the production of the predator population and show that sufficiently large delay can cause oscillations to persist via an Hopf bifurcation. We then consider a variable delay which will depend on the relative size of the prey population. Specifically, we find conditions on the functional form of the delay in which the branch of periodic solutions will be either sub- or super-critical as well as an accurate estimation of the amplitude. (flyer in PDF form)