On Monday, October 24, at 3:30 pm in Math Building 357, Dr. Brandy Doleshal will be talking about “Dehn Surgery and Knots in the Genus 2 Surface.”
Abstract: Low-dimensional topology is the study of 3- and 4-manifolds. A link is an embedding of some number of circles into a 3-manifold M. Each circle is called a component, and a link of one component is called a knot. Dehn surgery is a way of replacing a neighborhood of a component of knot or link to create a (possibly) new manifold. A classical result of Wallace and Lickorish tells us that any closed compact 3-manifold can be obtained by Dehn surgery on a link. Hence we can study 3-manifolds through studying knots and links. We will discuss some knots on the genus 2 surface and the Dehn surgeries they admit. (flyer in PDF form)
On Monday October 10th, at 3:30 PM in Math Building 357 Dr. Robert Strader will be talking about “Computer Arithmetic.” This talk will be accessible to all levels of students and computer users.
Abstract: Modern computation requires fast and correct operation for applications. The twin goals of performance and correctness are often at odds and require specialized algorithms and circuits for successful implementations. Come join us for an overview of representational systems, algorithmic techniques, and circuit designs. Representational methods include positional (place value system) notation in standard bases, redundant systems such as signed digit representation, and various specialized systems including irrational and logarithmic representations. Specialized algorithms for fast addition, multiplication and division have been developed for algorithmic operation. Extended internal systems can help to reduce errors. Many of these systems have found encodings in circuit designs for fast operation and correct computation. (flyer in PDF form)
On Monday September 12th at 3:30 in Math Building 357, Dr. Jackie Jensen-Vallin will be giving a talk on “Conway Notation and Gilbreath Knots.” This talk will be interesting and accessible for all levels of students. (flyer in PDF form)
Abstract: A knot is an embedding of a circle in three-dimensional space. The classification question – do two projections of knots represent the same knot – is a large question in knot theory, and many invariants have been developed to address this. We will focus our invariant discussion on the Conway notation and explore knots whose Conway notation correspond to Gilbreath sequences. A Gilbreath sequence is a sequence of (traditionally) natural numbers a_1, a_2, a_3, …, a_n such that all subsequences a_1, a_2, …, a_m with m≤ n contain consecutive natural numbers. We will ask if all knots can be built from Gilbreath sequences, and consider many examples.
Next Monday, April 11, at 3:30 in Math 357, Dr. Jonathan Mitchell will be talking about “Techniques for Analyzing Nonlinear Oscillators.”
Abstract: To the chagrin of many scientists, we live in a nonlinear world. We tend recognize patterns and formations in all sorts of contexts not the least of which is in the physical sciences. Many of the periodic motions we observe can be described using various systems of nonlinear differential equations. The aim of this talk is to highlight some of the techniques that are used to analyze such nonlinear oscillators as well as discuss some of the open questions on which we hope to shed some light in the future. (Flyer in PDF form)
Next Monday (April 4th) at 3:30 PM, Dr. Lesa Beverly will give a presentation titled “The Best Kept Secret: SFA Professional Development of Mathematics Teachers.”
Abstract: The Department of Mathematics and Statistics has a strong history of training mathematics teachers. In this presentation, we will explore the externally funded programs that have been a part of our departmental focus since 2000, including those that have been housed in the STEM Research and Learning Center. Successes and lessons learned from these experiences will be shared. Current projects, outreach efforts, and future opportunities will also be discussed. (flyer in PDF form)
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)
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.