Undergraduate Mathematics Symposium
Saturday, November 18, 2023
University of Illinois at Chicago

About the symposium

Download the symposium poster

Plenary lectures

• Claudia Miller (Syracuse University)
  Intersection numbers in algebraic geometry
  Abstract: 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
  Abstract: 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.

Poster session

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

Registration to attend the symposium has closed.

Schedule and locations

The symposium will be held in the Science and Engineering Offices (SEO) building. The full schedule can be found below.

• UIC Campus map
• SEO building: 851 S. Morgan St., Chicago, IL 60607

The schedule of events is shown below:

Previous symposia

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

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.

Acknowledgment

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