Thursday

Mini-course 1. From Here to There: Exploring Routes in Graphs and Sets

Lisa Naples

Abstract:  Suppose that we want to run some errands at various locations throughout town.  What is the most efficient way for us to travel from location to location and then return home? 

In this course, we will begin by exploring how ideas from graph theory can help us to answer this question.

We will then extend the task by assuming that we need to visit infinitely many locations. We will see that tools from statistics and calculus can sometimes be used to determine efficient routes through sets.  We will also explore situations in which these tools can fail to help us find a reasonable route.

Relevant background from graph theory, statistics, and calculus will be introduced in the course.

Mini-course 2. How Fermat's Last Theorem influenced modern number theory.

Alex Barrios

Fermat's Christmas Theorem

Abstract: On Christmas Day, 1640, Fermat wrote to Mersenne to inform him he had proven that every prime whose remainder is 1 after dividing by 4 is expressible as a sum of two squares. Fermat did not include a proof, but gave a challenge: "I would be very pleased if you made the effort of finding it, if only for learning whether I estimate my invention more highly than it deserves." The challenge mystified mathematicians for a century, and was finally set to rest by Euler in 1749. In this lecture, we trace Euler's proof of the sum of squares theorem.

Worktime

Informal conversation

Nicholas Wegman

Talk. What does a mathematician do in industry?

Nicholas Wegman

Abstract: Most mathematicians never become math professors. Does this mean you shouldn’t study math? Of course not! In addition to being fun, studying math opens a wide variety of career opportunities beyond academia and provides skills that are universally applicable. In this talk I will discuss how my team and I use machine learning and AI in the world of supply chain planning. Some common problems we tackle are predicting the sales of every item in a store, suggesting the amount of inventory to stock, and optimizing the price that will maximize revenue. Additionally, I’ll use my own experience of transitioning from academia to the corporate world to showcase what from studying math has been useful, what hasn’t been useful, and what I wish I had learned earlier in my career.