Undergraduate Mathematics Symposium
Saturday, November 2, 2019
University of Illinois at Chicago
Organized by David Dumas, Julius Ross, Christof Sparber, and Kevin Tucker
This page is about the
2019 symposium.
For the latest symposium information see the UMS home page.
About the symposium
The Undergraduate Mathematics Symposium at UIC is an annual oneday
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.
Download the symposium poster (designed by Jānis Lazovskis)
Plenary lectures
 Will Perkins (UIC)
Sphere packings, spherical codes, and hard spheres in high dimensions
Abstract:
What is the densest possible packing of identical spheres in Euclidean space? The answer to this very old question in mathematics is only known in dimensions 1, 2, 3, 8, and 24. In very high dimensions, the answer is almost a complete mystery. I will describe a connection between geometric packing problems such as this and an important probabilistic model from statistical physics: the hard sphere model in which gas molecules are represented by randomly placed nonoverlapping spheres. I will then present a new lower bound on spherical codes and kissing numbers in high dimensions.
 Eloísa Grifo (UC Riverside)
Symbolic powers and a story of algebra vs geometry
The equation
xy=0 describes two lines in 2dimensional space; many
other interesting geometric objects can be described by polynomial
equations. Hilbert's Nullstellensatz gives a correspondence between
such geometric objects, which are called varieties, and the sets of
equations that describe them, which have an interesting algebraic
structure of their own. According to this correspondence, varieties
are described by the polynomials that vanish at precisely all their
points... but how do we measure that vanishing?
We will give some answers, but find that many more questions are still open.
 Benoit Charbonneau (U Waterloo)
The dodecaplex and wonders of the fourth dimension
The dodecaplex is one of the regular solids in four dimensions. I cannot show it to you (the symposium budget doesn't cover extradimensional travel), but can describe many of its features, and show you projections. Prepare for a journey through history and through dimensions.
Transit and parking
The UIC campus is served by the CTA blue line train (UICHalsted stop) and many CTA bus lines.
Those driving may use any of the UIC visitor parking lots. Take a
ticket and we can give you a sticker that allows you to exit.
Schedule
Lectures are held in Lecture Center F4. Plenary lectures are 50 minutes and student lectures 20 minutes.
Registration, lunch, and breaks will all be held in Science and Engineering Offices (SEO) room 300. A catered lunch of sandwiches and salads is provided for all symposium participants.
The main symposium events are all held on Saturday, November 2. We are also offering an optional Friday afternoon poster showing at the UIC math department's weekly tea.
The full schedule of events is as follows:
Friday, November 1 
4:00  5:00pm 
Optional: UMS posters can be displayed at UIC math department tea in SEO 300

Saturday, November 2 
8:15  8:50am 
Signin and coffee in SEO 300 
Morning session — Plenary
Lectures — Lecture Center F4 
9:00am 
Will Perkins  Sphere packings, spherical codes, and hard spheres in high dimensions 
10:00am 
Benoit Charbonneau  The dodecaplex and wonders of the fourth dimension 
11:00am 
Eloísa Grifo  Symbolic powers and a story of algebra vs geometry 
12:00pm 
Lunch in SEO 300 
Afternoon Session 1 — Student
lectures — Lecture Center F4 
1:00pm 
Mary Stelow  Complexity of SAdic Sequences Associated with Some Multidimensional
Continued Fractions 
1:25pm 
Kelly Chen  Unusual Topographical Features of Laplacian Eigenfunctions 
1:50pm 
Talia Blum  Unlikely Intersections and Portraits of Dynamical Semigroups 
2:15pm 
Coffee break 
Afternoon session 2 — Student
lectures — Lecture Center F4 
2:45pm 
Alexandra Newlon  The Fibonacci Quilt Game 
3:10pm 
Julinda Mujo  Smocked Metric Spaces and their Tangent Cones 
3:35pm 
Dylan King  The Distribution of Missing Sums in Correlated Sumsets 
4:00  5:30pm 
Poster Session 
Acknowledgment
UMS is supported in part by the following grants from the National Science Foundation: NSF RTG 1246844, DMS 1348092 CAREER.