Undergraduate Mathematics Symposium
Saturday, October 24, 2015
University of Illinois at Chicago

About the symposium

The 2015 UMS was held at UIC on Saturday, October 24.

Download the symposium poster

Plenary lectures

• Chelsea Walton (Temple University)
  Hamilton's quaternions
  Abstract: 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.
• Henry Segerman (Oklahoma State University)
  How to make sculptures of 4-dimensional things
  Abstract: 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.
• Jayadev Athreya (UIUC)
  Density in Apollonian packings
  Abstract: 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.

Location

• Google Maps view of SEO and UIC campus (online, interactive)
• Campus maps from UIC Facility Information Management (PDF and image downloads)

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 participants.

8:15 - 8:50am	Sign-in and coffee in SEO 300
Morning session — Plenary Lectures — SEO 636
8:55am	Opening remarks
9:00am	Jayadev Athreya (UIUC) — Density in Apollonian packings
10:00am	Chelsea Walton (Temple University) — Hamilton's quaternions
11:00am	Henry Segerman (Oklahoma State University) — How to make sculptures of 4-dimensional things
12:00pm	Lunch in SEO 300
Afternoon Session 1 — Student lectures — SEO 636
1:00pm	Yao-Rui Yeo (University of Minnesota) — The Hurwitz Existence Problem
1:30pm	John Spaw (Millikin University) — Locating Numbers and Sets for Disconnected Graphs
2:00pm	Alex Page (UIUC) — The Broken Stick Problem in Higher Dimensions: From a Classic Puzzle to Modern Distance Geometry
2:30pm	Coffee break in SEO 300
Afternoon session 2 — Student lectures and Poster Session — SEO 636 and SEO 300
3:00pm	Elena Malloy (Yale University) — Quasi-synchronization on a fractal network of logistic maps
3:30pm	Ben Lowe (University of Chicago) — Configuration Spaces of Hinge Structures and Singularities
4:00 - 5:00pm	Poster Session in SEO 300

Previous symposia

2014

2013

2012

2011

2010

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