Undergraduate Mathematics Symposium
Saturday, October 15, 2016
University of Illinois at Chicago

About the symposium

The 2016 UMS was held at UIC on Saturday, October 15.

Download the symposium poster

Plenary lectures

• Sarah Koch (Michigan)
  Mating habits of polynomials
  Abstract: Given two suitable complex polynomial maps, one can construct a new dynamical system by mating the polynomials; that is, by "gluing" the polynomials together in a dynamically meaningful way. In this talk, we focus on quadratic polynomials — we begin with a brief discussion of parameter space for quadratic polynomials (where the Mandelbrot set lives), we then define the mating of two quadratic polynomials, and finally we explore examples where the mating does exist, and examples where it does not. There will be many pictures and movies in this talk.
• Andrew Putman (Notre Dame)
  The geometry of tilings
  Abstract: I will discuss the connections between tilings (especially of the plane) and geometry, dynamics, and computability.
• Richard Schwartz (Brown)
  5 points on a sphere
  Abstract: Thomson's 5-electron problems asks how 5 electrons will arrange themselves on a sphere so as to minimize their total electrostatic potential. A generalization of Thomson's problem asks the same question when the points repel each other according to a different power law potential. I recently proved that the triangular bi-pyramid is the best configuration when the power law exponent is less than about 15.04807 and then the answer switches to a pyramid with square base. In my talk I'll sketch my result and also show computer demos illustrating the ideas.

Location

• Google Maps view of SEO and UIC campus (online, interactive)
• Campus maps from UIC Facility Information Management (PDF and image downloads)

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, October 14
4:00 - 5:00pm	Poster previews and math department tea in SEO 300
Saturday, October 15
8:15 - 8:50am	Sign-in and coffee in SEO 300
Morning session — Plenary Lectures — SEO 636
9:00am	Sarah Koch — Mating habits of polynomials
10:00am	Andrew Putman — The geometry of tilings
11:00am	Richard Schwartz — 5 points on a sphere
12:00pm	Lunch in SEO 300
Afternoon Session 1 — Student lectures — SEO 636
1:00pm	Stephanie Mui — Isometric Embedding of a Flat Torus in 3D Euclidean space
1:30pm	Maithreya Sitaraman — A symmetrization process to characterize Lights Out setups
2:00pm	Christian Borst — Probability of Reducibility of Random Polynomials as Degree Increases
2:30pm	Coffee break in SEO 300
Afternoon session 2 — Student lectures and posters — SEO 636
3:00pm	Timothy Alland — A Pattern Avoidance Criteria for Parabolic Fiber Bundle Structures of Schubert Varieties
3:30pm	William Vickery — Patterns Relating Self Instersection Number and Word Length for Curves in the Three Punctured Sphere
4:00 - 5:00pm	Poster Session in SEO 300

Previous symposia

2015

2014

2013

2012

2011

2010

Contact