The Vanderbilt Undergrad Seminar

The Undergraduate Seminar in Mathematics is a weekly, hour long talk. There you can hear about some of the many deep and interesting areas of mathematics beyond what you would see in the classroom of most math classes. The talks are designed to be accessible to any college student; little to no math background is required. The seminar occurs most weeks on Tuesday from 6-7pm, in Stevenson 1206. Come by and enjoy some pizza and soda before the talk, and hear about something new. We hope to see you there!

This semester’s talks: (This list will be updated as talks are scheduled.)

September 18: Sandeepan Parekh
Title: Polygons and polyhedrons in space and beyond
Abstract: How many regular polygons are there? Equilateral triangles, squares … as many as you like. Surprisingly, the answer to how many regular solid polyhedrons (3D version of polygons) there are, is a mere 5! I shall prove why there are just five of these Platonic Solids and attempt to argue that there ought to be more, hidden in hyperbolic space.

September 25: Hayden Jananthan
Title: This Title is False
Abstract: To some, Gödel’s name is synonymous with the disruption of mathematics in the early 1900s, due in part to his famous ‘Incompleteness Theorems’, which put bounds on the expressiveness of formal systems of arithmetic. Frequently misunderstood and misstated, we will formally describe what Gödel’s First Incompleteness Theorem states and give a sketch of its proof. Analyzing our proof closely, we will find an even more general statement that both deepens and clarifies our original statement of his theorem.

October 16: Michael Montgomery
Title: Knot a Problem
Abstract: If you have ever put a pair of headphones in your pocket, you know what it is like to be confronted with a tangled mess and no clear way to untie it. Much like your knotted headphones, knot theory looks difficult to untangle, but with some mathematical techniques we can begin to unravel it. We will see how to tell knots apart, how to add them together, and show that no knot can be unraveled by adding a second knot

October 23: Glenn Webb
Title: Spatial Spread of Epidemic Diseases in Geographical Settings
Abstract: Deterministic models are developed for the spatial spread of epidemic diseases in geographical settings. The models are focused on outbreaks that arise from a small number of infected hosts imported into sub-regions of the geographical settings. The goal is to understand how spatial heterogeneity influences the transmission dynamics of the susceptible and infected populations. The models consist of systems of partial differential equations with diffusion terms describing the spatial spread of the underlying microbial infectious agents. Applications are given to seasonal influenza epidemics.

October 30: Larry Schumaker
Title: Splines: A case study on the impact of Mathematics
Abstract: Functions are the key mathematical tool for describing and analyzing
the world around us.  For centuries, mathematicians have been looking
for the right kinds of functions to do this job.  For years,
polynomials played the most prominent role.   But starting  in the
1960’s it was realized that a kind of piecewise  polynomial,
called a spline, could be a much more effective tool, especially
in the context of high speed computing.  Since then dozens of
books and many thousands of research papers have been written
on this new mathematical idea, and the number of applications
have grown exponentially.

In this nontechnical talk I will show how this relatively new
mathematical development impacts our every day lives in a
variety of unexpected ways, and how it has led to powerful new
technologies with major economic and societal impacts in all kinds
of areas including communications, engineering, finance, medicine, and
the sciences, to name a few.

Novermber 6: Ryan Solava
Title: Voting Troubles
Abstract: The basic system of voting where everyone chooses one option, and the option with the most votes wins seems like the obvious way of doing things. But is there another way? On this Election Day, we’ll explore other possible ways of making a choice based on a group’s preferences and see the consequences these systems have.

November 13: Andy Jarnevic
Title: Combinatorial Game Theory
Abstract: For as long as there has been civilization, people have been inventing and playing games. Games such as chess, checkers and go have captured imaginations for centuries. The complex structures that can emerge from these simple rules has led to the creation of new mathematical ideas to help analyze and solve games. In order to understand these tools and techniques we will discuss and play four simple games that help shed light on combinatorial game theory.

November 27: Zack Tripp
Title: Using Calculus to Study Numbers
Abstract: In this talk, I will give a brief outline of what analytic number theory is. We will see how we can use calculus, which is often used to study objects that are continuous, in order to find out more about prime numbers, which are discrete in nature. In particular, I will describe some of the major results that have defined the field, as well as some of the most interesting open questions. As we will see, one of the most fascinating aspects of analytic number theory is that the problems are often easy to state but difficult to say much about. However, we will also see that there has been exciting progress recently on one such problem called the Twin Prime Conjecture.

Check out all of the awesome talks we have had in the past!