Undergraduate Mathematics Symposium
Saturday, October 24, 2015
University of Illinois at Chicago
Organized by Alex Austin, David Dumas, Steven Hurder, and Kevin Tucker
This page is about the 2015
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, as well as contributed lectures and posters by undergraduates on their own research projects.
The 2015 UMS was held at UIC on Saturday, October 24.
Download the symposium poster
In this talk I will discuss the last great achievement of Sir William Rowan Hamilton- the discovery of the quaternion number system. This discovery was very controversial for its time and nearly drove Hamilton mad! The talk will be full of drama, intrigue, and wonderful mathematics. Some familiarity with the complex number system would help, but is not needed.
Segerman (Oklahoma State University)
How to make sculptures of 4-dimensional things
Our brains have evolved in a three-dimensional environment, and so we are very good at visualising two- and three-dimensional objects. But what about four-dimensional objects? The best we can really do is to look at three-dimensional "shadows". Just as a shadow of a three-dimensional object squishes it into the two-dimensional plane, we can squish a four-dimensional shape into three-dimensional space, where we can then make a sculpture of it. If the four-dimensional object isn't too complicated and we choose a good way to squish it, then we can get a very good sense of what it is like. We will explore the sphere in four-dimensional space, the four-dimensional polytopes (which are the four-dimensional versions of the three-dimensional polyhedra), and various sculptures, puzzles, and virtual reality experiences that have come from thinking about these things.
Density in Apollonian packings
We describe how to compute different notions of density in Apollonian circle and sphere packings, and an unexpected connection to the Riemann Hypothesis. This is work that grew out of an IGL project with Jason Hempstead, Kaiyue Hou, Danni Sun, and Joe Vandehey, and also encompasses joint work with Cristian Cobeli and Alexandru Zaharescu.
All symposium events take place in the Science and Engineering Offices building (SEO) on UIC's East Campus. Registration, lunch and coffee are provided in room 300, while the lectures 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
||Jayadev Athreya (UIUC) — Density in Apollonian packings
||Chelsea Walton (Temple University) — Hamilton's quaternions
||Henry Segerman (Oklahoma State University) — How to make sculptures of 4-dimensional things
||Lunch in SEO 300
|Afternoon Session 1 — Student lectures — SEO 636
||Yao-Rui Yeo (University of Minnesota) — The Hurwitz Existence Problem
||John Spaw (Millikin University) — Locating Numbers and Sets for Disconnected Graphs
||Alex Page (UIUC) — The Broken Stick Problem in Higher Dimensions: From a Classic Puzzle to Modern Distance Geometry
||Coffee break in SEO 300
|Afternoon session 2 — Student
lectures and Poster Session — SEO 636 and SEO 300
||Elena Malloy (Yale University) — Quasi-synchronization on a fractal network of logistic maps
||Ben Lowe (University of Chicago) — Configuration Spaces of Hinge Structures and Singularities
|4:00 - 5:00pm
||Poster Session in SEO 300