Undergraduate Mathematics Symposium
Saturday, November 18, 2023
University of Illinois at Chicago
Organized by David Dumas and Kevin Tucker
About the symposium
The Undergraduate Mathematics Symposium at UIC is an annual one-day
meeting focusing on undergraduate mathematical research and
education. The meeting features plenary lectures by mathematical
researchers and a poster session where students present results from undergraduate mathematical research projects.
Download the symposium poster
The 2023 UMS will be held in person on the UIC campus.
- Claudia Miller (Syracuse University)
Intersection numbers in algebraic geometry
We take a look at curves, surfaces, and higher dimensional spaces defined by polynomial equations, focusing especially on how they intersect.
You have seen double, triple, and higher roots of a polynomial, tangent circles, and other instances of intersection.
We will recall these and look at a more dynamic version of these ideas.
This involves looking at 3-dimensional (and higher) pictures and understanding how to measure the multiplicity of an intersection using abstract algebra—all of which will be revealed (and explained from scratch) in the talk.
In the process, we will also cover a bit of the history in the development of the correct measure of these intersections, back to algebraic geometers in late 19th century Italy, ending with the breath of fresh air in the 1950s with Serre's revolutionary algebraic reformulation via Euler-Poincaré characteristics, and various vanishing/nonvanishing conjectures of Serre, solved and unsolved.
- Priyam Patel (University of Utah)
Curves and Surfaces in Topology
Topology is a branch of mathematics primarily concerned with studying the shape of spaces.
I will begin this talk by giving you a more detailed description of what topology is and how it differs from the more familiar subject of geometry.
One of the fundamental goals in topology is determining when two objects are "topologically" the same or different.
For example, a circle and an ellipse are geometrically different objects, but they are actually considered to be the same object by a topologist.
For much of the talk, I will focus on a class of objects called surfaces.
We will see that there is a rich theory of curves on surfaces, and that this theory can help us determine when two surfaces are topologically different.
Undergraduates who have completed an REU, summer program, or other supervised mathematical research experience can apply to present a poster at UMS.
Deadline: October 18 was the deadline for full consideration. Applications are now closed.
Attending the symposium
Everyone is welcome to attend, but please register so we know to expect you.
Funding: We do not have travel funding for non-presenter participants.
Schedule and locations
The symposium will be held in the Science and Engineering Offices (SEO) building. The full schedule can be found below.
The schedule of events is shown below:
|Saturday, November 18
|9:00 - 9:30am
|Sign-in and coffee
|Plenary lecture: Claudia Miller
|Morning poster session
|Plenary lecture: Priyam Patel
Code of Conduct
Speakers and participants in UMS must agree to the UMS Code of Conduct. Its purpose is to help the organizers ensure a safe, respectful, and welcoming environment for everyone.
UMS is supported in part by a grant from the National Science Foundation: NSF RTG 2037569.