Events

Dr. Aaron Lauve, Loyola University
Flow Polytopes and Integer Sequences
Wed. Feb. 26th at 4pm
120 Kirby Hall

Abstract: Suppose you wish to optimize the transport of some material through a network, given a number of constraints. (Think: how can I best move 2000 barrels of oil from Houston to Charlotte, if I should pick up 500 along the way in New Orleans and drop off 1000 in Atlanta?) To get started, it seems appropriate to define your “search space.” Enter flow polytopes. These geometrical objects encode all the ways that material can flow through directed networks. While these polytopes arose in the field of optimization, they have since piqued the interest of mathematicians in numerous fields (mathematical physics, representation theory, and tropical geometry, to name three). In this lecture, I hope to pique yours as well! As we work our way through basic examples (and connections to these other fields), we’ll stumble on a number of interesting questions. Some of which we’ll even be able to answer in an immensely satisfying way, such as: how can you determine the dimensions, vertices, and volume of these polytopes? Here’s another: how are the famous Fibonacci numbers and Euler numbers related? (While this lecture is mainly intended as a survey, I will share some new results found in joint work with Rafael Gonzalez d’Leon and his undergraduate student, Anuraj Nair.)