Undergraduate Mathematics Symposium
Saturday, October 5, 2013
University of Illinois at Chicago
Organized by Alex Austin, David Dumas, and Steven Hurder
This page is about the 2013
For the latest symposium information see the UMS home page.
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 invited lectures by mathematical researchers and contributed lectures by undergraduates on their own research projects.
The next UMS will be held at UIC on Saturday, October 5, 2013.
Jim Fowler (Ohio State)
Given a field (a number system), we can build a "geometry" --- something with points and lines. For instance, starting with the field of real numbers, we consider ordered pairs of reals, and we get the Cartesian plane.
What if we instead started with the geometry? Could we, from the points and lines, recover a field? Sometimes, yes! The geometries we start with will be "projective geometries" where any two lines meet, maybe "at infinity". How do we then get a field? Commutativity of multiplication --- among the other axioms for a field --- are encoded as gloriously complicated diagrams of points and lines. Desargues' theorem and Pappus' theorem show up to save the day.
A reference is Hilbert's Grundlagen der Geometrie.
Irina Nenciu (UIC)
Modeling with Randomness
I will describe several surprising real-life and mathematical instances in which models involving randomness provide excellent descriptions for deterministic situations. The main mathematical tool are random matrices, which live at the intersection of linear algebra and probability theory. I will describe these objects, and some of the expected, and the utterly unexpected, instances in which they are used.
Lev Reyzin (UIC)
Three Great Ideas in Computing
Abstract: I will talk about three surprising mathematical ideas that have revolutionized computer science and had enormous impact on our society. To give a broad perspective, I will jump from computability theory to cryptography and then to machine learning. I will also describe some current research directions and open problems in these areas.
All symposium events will take place in the Science and Engineering Offices building (SEO) on UIC's East Campus. Registration, lunch and coffee will be provided in room 300, while the lectures will take place in room 636.
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
|8:15 - 8:50am
||Sign-in and coffee in SEO 300
|Morning session — Plenary Lectures — SEO 636
||Lev Reyzin (UIC) — Three Great Ideas in Computing
||Jim Fowler (Ohio State) — Projective Planes
||Irina Nenciu (UIC) — Modeling with Randomness
||Lunch in SEO 300
|Afternoon Session 1 — Student lectures — SEO 636
||Ayah Almousa (Wisconsin-Madison) — Counting Polynomials with Given Root Multiplicities
||Derek Francour (Wisconsin-Madison) — Computing the Shape of Configuration Spaces
||Weston Ungemach (Chicago) — A Better Bound on the Size of Isospectral Families
||Kelsey DiPietro (UIC) — Negative Snell's Law
||Coffee break in SEO 300
|Afternoon session 2 — Student lectures — SEO 636
||Lisa Gullo (Dominican) — Optimal Paths in Graphs with Variable Weights
||Bradley Lewis Burdick (Ohio State) — A Simplicial Tutte Flows Conjecture
||Rachel Katz (Chicago) — The Colored Cubes Problem