Midwest Undergraduate Mathematics Symposium
University of Northern Iowa
Friday, April 12, 2013, 7:00pm
Shorter or Rounder? A Visual Tour of Curve Shortening
Abstract: Imagine a long, not especially stretchy, rubber band laid out on a table. It might have lots of spirally loops, or cross over itself, just don’t allow it to have any sharp kinks. The picture you get is an example of a simple closed curve. The curve shortening flow is a geometric way of trying to even out the bends.
Curve shortening is part of a family of problems in geometry that takes inspiration from famous old differential equations (like the heat equation), and includes things like the spectacularly amazing Ricci Flow, which was recently used by Perelman to settle the Poincare conjecture in three dimensions (and more).
We shall look at some of the fun things known about curve shortening. And we shall also look at simple variants of curve shortening where things should be simpler, but are not as yet as well understood.
There will be lots of pictures and examples, and maybe just a little bit of calculus and geometry.
Saturday, April 13, 2013, 9:00am
Optimizing Golf Bag Locations
Abstract: We model the behavior of a walking golfer who must decide where to leave his or her golf bag when approaching a green to putt. The goal is to minimize the amount of walking (and hence the amount of time) necessary to finish the hole and move on to the next tee.
Funding for MUMS 2013 is provided by NSF grant DMS-0846477 through the MAA Regional Undergraduate Mathematics Conferences program (maa.org/RUMC). Additional funding is provided by the Simpson College Mathematics Department (simpson.edu/math).