# Undergraduate Mathematics SymposiumSaturday, November 10, 2018University of Illinois at Chicago

Organized by David Dumas, Julius Ross, and Kevin Tucker

The Undergraduate Mathematics Symposium at UIC is an annual one-day meeting focusing on undergraduate mathematical research and education. The meeting features invited lectures by mathematical researchers, as well as contributed lectures and posters by undergraduates on their own research projects.

### Plenary lectures

• Nathan Kaplan (UC Irvine)
Dudeney's No-Three-In-Line Problem
Abstract: What is the maximum number of points in an n x n grid such that no 3 points lie on a line? Here we mean not just vertical, horizontal, and diagonal lines, but lines of any slope. Dudeney introduced this simple sounding problem in 1917, but it is still mysterious today. We will discuss bounds for this problem and a conjectural answer due to Guy and Kelly. Along the way we will see ideas from number theory and algebraic geometry, and many computational and algorithmic directions to explore.
• Richard Kenyon (Brown)
The shape of a large integer partition
Abstract: A partition is a way to write a positive integer as a nonincreasing sum of smaller positive integers: 7=3+2+2 for example. How many partitions does a large integer have? What does a "typical" partition look like?
• Dhruv Mubayi (UIC)
From Ramsey theory to arithmetic progressions and hypergraphs
Abstract: I will begin by giving a brief introduction to Ramsey theory, in layman's terms, and describing one of the most well-known open problems in this area. This will naturally lead to a similar question about arithmetic progressions in the integers. Finally, we will see a glimpse of how these problems about arithmetic progressions are solved by modern combinatorial methods using hypergraphs.

### Location

All symposium events will take place on UIC's East Campus, in the Science and Engineering Offices building (SEO) and in Lecture Center F1. Registration, lunch and coffee will be provided in room SEO 300, while the lectures will take place in the lecture center.

### Schedule of events

Plenary lectures are 50 minutes and student lectures 20 minutes; breaks of 10 minutes between talks allow for questions and discussion. A catered lunch of sandwiches and salads is provided for all symposium participants.

 Friday, November 9 4:00 - 5:00pm Poster previews and math department tea in SEO 300 Saturday, November 10 8:15 - 8:50am Sign-in and coffee in SEO 300 Morning session — Plenary Lectures — Lecture Center F1 9:00am Dhruv Mubayi - From Ramsey theory to arithmetic progressions and hypergraphs 10:00am Richard Kenyon - The shape of a large integer partition 11:00am Nathan Kaplan - Dudeney's No-Three-In-Line Problem 12:00pm Lunch in SEO 300 Afternoon Session 1 — Student lectures — Lecture Center F1 1:00pm Gabriel Flores - A Priori Simulation of a Smart-Navigated UAV Disaster Cargo Fleet 1:30pm Marisa Gaetz - Anti-power j-fixes of the Thue-Morse word 2:00pm Katie Gallagher - Generating functions for power moments of elliptic curves over Fp 2:30pm Coffee break in SEO 300 Afternoon session 2 — Student lectures — Lecture Center F1 3:00pm Seth Colbert-Pollack - Shift operators on directed infinite graphs 3:30pm Alexander Vetter - Deformations of the Weyl Character Formula via Ice Models 4:00pm Maxine Calle - Putting the "k" in Curvature: k-Plane Constant Curvature Conditions 4:30 - 5:30pm Poster Session — SEO 300

### Contact

Julius Ross (juliusro@uic.edu)