GWU Mathematics Department Graduate Student Seminar
SPRING 2009 - Seminar Presentations

Bill Schmitt, Hao Wu, and Navin Vembar (CNA), 1 May 2009.

Annual Employment Search Panel

All graduating BA, MA and PhD students are encouraged to attend and gain perspective on the job market for mathematicians. Undergraduates should note, however, that most of the panel's discussion will be geared toward graduate level employment. The panel will offer advice and answer questions that attendees may have. Junior graduate students are also encouraged to attend in order to learn about the documents needed for the job market, the accomplishments that employers look for and other items of interest for the employment search.

Click here to see the department's "Job Search Web Page"

Radmila Sazdanovic, 24 April 2009.

Categorification and SLarc Algebra

Categorification lifts numbers to vector spaces and vector spaces to categories. A basic example is the turning of Euler Characteristics of a topological space into its homology groups. More exotic examples include various link homology groups which lift polynomial invariants of knots, such as Khovanov Homology. I will introduce a calculus of planar diagrams that leads to the categorification of basic one variable polynomials.


Mike Coleman, 17 April 2009.

Paper Folding and Polyhedral Origami

There will be very little mathematics in this presentation since I'm neither an Algebraist nor a Topologist. Both of these subjects are the branches of mathematics that realize the application of interest: the construction and design of polyhedral origami. I'll present a few elements and modules that can be used to generate all sorts of interesting polyhedron. I hope that this will be an enjoyable hour that may spark some artistic creations around the department's ceilings! Undergraduates are also encouraged to attend.


Yongwu Rong, 10 April 2009.

Mathematics is Beautiful! Mathematics is Useful!

During different stages of my life, I have had various views of mathematics:

Mathematics is boring, but I can do it. (elementary school)
Mathematics is fun, but is often hard. (middle school)
Applied math is useful; pure math is useless. (undergraduate student)
Pure math is beautiful; applied math is ugly. (graduate student)
Mathematics is beautiful; mathematics is useful. (college professor)

This talk will be a joint exploration of mathematics through the beauty of polyhedra, knots, tiling, Poincare's dodecahedral space, as well as their applications in biology, computer graphics, cosmology, engineering, and more. This is an opportunity to appreciate some of the latest mathematical developements in the twenty-first century that you can compare against the seventeenth century mathematics of your calculus course.


Vincent Guingona, University of Maryland. 20 February 2009.

An Introduction to Model Theory

I will discuss an application of my work in Model Theory to an area of Computer Science known as Learning Theory. I will discuss basic definitions and a few results. After that, I will discuss the Model Theory behind the scenes and explore the connections it shares with Learning Theory.


Jennifer Chubb, 30 January 2009.

Fractals!

This is going to be a fun talk with lots of pictures. If you know what complex numbers are and can compute a limit, you'll be all set :) .


Kouki Taniyama, Waseda University and GWU Topology. 23 January 2009.

Regular Projections of Knots

A knot is a simple closed curve embedded into a three-dimensional Euclidean space. A regular projection of a knot is its shadow on the two-dimensional Euclidean plane under a natural projection. A knot can be deformed into another knot that might look different from the original knot. Then the new knot may have a different regular projection. We consider the set of all regular projections obtained from a knot in such ways. We will discuss some problems on this infinite set of the regular projections of a knot. We will show some applications that is joint work with Professor Jozef Przytycki.


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