The Vanderbilt Undergrad Seminar

The Undergraduate Seminar in Mathematics is an hour long talk, held every other week. 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 5:30-6:30pm, in Stevenson 1320. 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.)

January 31: Sam Shepherd
Title: The boundary at infinity
Abstract: Given a metric space, like the plane, one can imagine points at infinity, with one point at the end of each geodesic ray. Together these points form the boundary at infinity for the space. I will describe several examples of spaces where we can construct the boundary at infinity, and discuss some important properties.

February 21: Denali Relles
Title: Cantor’s function, or: why derivatives are weird
Abstract: In mathematics we love weird things. They let us say, “Why is this weird?” and “What else is weird?” and “Should this be allowed?”. Even in topics you may already know, like derivatives, you have to be careful about the specifics. In this talk, I will talk about a certain function called “Cantor’s Staircase,” and explain why it is weird. Then, I’ll discuss how we deal with this as mathematicians by saying certain things are allowed and certain things aren’t.

March 7: Hengrong Du
Title: Entropy: how do we measure uncertainty?
Abstract: The concept of entropy appears frequently in the physical and mathematical literature. It is often recognized as the entropy function xlogx. In this talk, I will introduce the axioms for measuring uncertainty or disorder and derive the entropy function from those axioms. Furthermore, I will discuss the maximum entropy principle in statistical physics.

March 28: Peter Huston
Title: Uses of the Perron-Frobenius theorem
Abstract: Matrices with only non-negative entries show up frequently in mathematics and in the real world. The Perron-Froebenius theorem shows that the largest eigenvalue of such a matrix is positive, and corresponds to an eigenvector with positive entries. We will examine the geometric reality behind this apparently algebraic result, and see a diverse host of applications in mathematics and other fields.

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