2017-2018 Mathematics Colloquia Titles, abstracts, times, and locations for the 2017-2018 mathematics colloquia at Washington and Lee University.

Winter 2018

The many ways to knot a tie.

  • Speaker: Elizabeth Denne (Washington & Lee University)
  • March 27th at 4:30pm in Robinson Hall 105
  • Refreshments at 4:00 pm in Robinson Hall foyer
  • Abstract: This talk is an exploration of knot theory and the number of ways to knot a tie. Random walks are used to show there are 85 ways to tie a standard tie with a flat facade. In The Matrix Reloaded movie, the Merovingian character wore a Trinity Knot, which is tied with the narrow end of a tie and where the facade is textured with many surfaces. When restrictions on ties are loosened, there turn out to be many more possible ways to knot a tie - over 266,682 at last count.

Ultra-mathematics

  • Speakers: Stephen Hardy (Washington and Lee University)
  • Wednesday, March 14th at 4:30 pm in Robinson Hall 105
  • Refreshments at 4:15pm in Robinson Hall foyer
  • Abstract: This talk is a friendly introduction to the alluring realm of ultra-mathematics using ultrafilters, ultralimits and ultraproducts. We will learn how to construct a finitely-additive probability measure on the integers, new and improved types of limits, and the hyperreals.

Fall 2017

Cauchy’s theorem and rigidity of circle polyhedra in the 2-sphere.

  • Speaker: John Bowers (James Madison University)
  • November 30th at 4:00 pm in Robinson Hall 105
  • Refreshments at 3:40 pm in Robinson Hall foyer
  • Abstract: This talk is two stories given in 3 acts. In Act I, I will present some of the rich history of the study of polyhedra, from Euclid on to the present day. In particular, I will sketch the proof of Cauchy's celebrated rigidity theorem for convex polyhedra in Euclidean space--most certainly a "proof from the book". In Act II, I will discuss the development of geometry beyond Euclid and the ancient geometers. Our focus will be on introducing two alternatives to Euclidean geometry--hyperbolic geometry, and the inversive geometry of circle packings on the sphere. We will explore the basic concepts, and discuss the connections between them. Finally, in Act III, we will sketch how the beautiful proof of Cauchy's can be generalized to prove a result of interest to the modern study of circle packings on the sphere. No prior knowledge beyond basic concepts from Euclidean geometry are assumed. 

What We Did Last Summer (Parents and Family Weekend Event)

  • Speakers: W&L Math students Aaron Schmitt, Justin Pusztay, Austin Jennings, Luke Farley and Hung Chu 
  • September 30th at 4:40 pm in Robinson Hall 105
  • Refreshments at 4:20 pm in Robinson Hall foyer
  • Abstract: The students will talk about their summer research.