Undergraduate Mathematics Symposium
Saturday, October 18, 2014
University of Illinois at Chicago

About the symposium

The next UMS will be held at UIC on Saturday, October 18, 2014.

Download the symposium poster

Plenary lectures

• Jerry Bona (UIC)
  Mathematics and the Ocean
  Abstract: Several currently interesting problems in oceanography will be outlined and particular issues isolated for study. These issues arise from questions in tsunami propagation, rogue wave formation and beach protection. We propose to investigate these issues by mathematical modeling. This will take us on a brief excursion into the realm of modeling ocean waves. The models will then be applied to cast light on the problems introduced at the outset.
• Amanda Knecht (Villanova)
  Ready for Hailstones in a Cloud? The 3n+1 Problem
  Abstract: Starting with an integer n greater than one, we can form a sequence in the following way. If n is even, divide it by two. If n is odd, multiply it by three and add 1. Repeat this process until your output is one. For example, if n = 3 the sequence of numbers outputted is 3; 10; 5; 16; 8; 4; 2; 1 and the sequence is 9; 28; 14; 7; 22; 11; 34; 17; 52; 26; 13; 40; 20; 10; 5; 16; 8; 4; 2; 1 when n = 9. These are sometimes called Hailstone sequences because they go up and down just like a hailstone in a cloud before crashing to the ground. It seems from experimentation that these sequences always eventually end in a one, and in 1937 Lothar Collatz conjectured that they always do. Now seventy-seven years later we still do not know if they do. In this talk I will present some of what we do know about this conjecture.
• Marie Snipes (Kenyon College)
  Mating Fractals: What do you get when you cross an airplane with a rabbit?
  Abstract: The field of complex dynamics has produced a host of interesting fractals with exotic names such as The Rabbit, The Airplane, and The Dragon. In this talk we will introduce how these beautiful objects arise as the so-called Julia sets of complex functions. We will then describe how two such fractals can be combined, or mated with each other to produce a new fractal, and how all of this is related to iteration of complex functions.

  Location

  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.

  • 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	Jerry Bona (UIC) — Mathematics and the Ocean
  10:00am	Amanda Knecht (Villanova) — Ready for Hailstones in a Cloud? The 3n+1 problem
  11:00am	Marie Snipes (Kenyon) — Mating Fractals: What do you get when you cross an airplane with a rabbit?
  12:00pm	Lunch in SEO 300
  Afternoon Session 1 — Student lectures — SEO 636
  1:00pm	David Buzinski (Case Western) — Rubiks Groups of Polyhedra and Polychora
  1:30pm	Yiwang Chen (UIUC) — Power Series with Number-theoretic Coefficients
  2:00pm	Alexander Dunlap (University of Chicago) — Generalizing Bolle's Classification of Multitilers to Three Dimensions Using Fourier Analysis
  2:30pm	Jasmine Otto (UIC) — Agent-Based Predator-Prey
  3:00pm	Coffee break in SEO 300
  Afternoon session 2 — Student lectures — SEO 636
  3:30pm	Shelby C. Kilmer (Bucknell University) — Random Groups at Density 1/2
  4:00pm	Elliot Kaplan (Ohio University) — Knot Depth for Positive Braids
  4:30pm	Nicholas Miller (University of Missouri-Columbia) — Smale Mean Value Conjecture for Quartic Polynomials
  5:00pm	Lev Kendrick (Walter Payton College Prep) — On the Lower Central Series Quotients of a Quotient of a Free Algebra

  Previous symposia

  2013

  

  2012

  

  2011

  

  2010

  

  Contact

  For further information, please contact David Dumas (ddumas@math.uic.edu).