Friday, October 13, 2006
Speaker: Shawn Westmoreland

Title: Manifolds

Abstract: This is an introduction to the idea of a manifold. Nothing deep here, I'll just be introducing some basic concepts.

Title: An introduction to free boundary problems

Abstract: I'll discuss what a free boundary problems is, how in certain settings they arise as better models than partial differential equations, and finally I'll discuss some of the purely mathematical challenges that come along with them.

Title: Remarks on nonlinear elliptic PDE's

Abstract: We will motivate the study of linear and nonlinear elliptic PDEs (Laplacian and Monge-Ampere), some of their properties and applications.

Title: An introduction to the obstacle problem.

Abstract: I am going to introduce the obstacle problem which arises as a simple model for when an elastic membrane is pulled down over a rigid body. The obstacle problem is one of the simplest free boundary problems, but it still leads to some important mathematics.

Title: When flatness implies smoothness

Abstract: We will discuss a generalized notion of smoothness called "Reifenberg flatness" used for sets which are too messy to have a genuine tangent plane.

Title: An application of Brunnian link

Title: Discussion of "Combinatorial Homotopy" by J.H.C. Whitehead.