Time, Place, etc:

Time: Tuesdays, 3:00 - 5:00

Place: Neill Hall, room 132

Credit: variable 1-3, graded

Structure: ongoing research seminar

What we are currently doing:

Fall 2009, we will begin by working through Do Carmo's book titled "Riemannian Geometry". After that, we will glean insights and techniques from De Lellis's 2008 monograph "Rectifiable Sets, Densities and Tangent Measures" and Federer's 1959 paper "Curvature Measures".

Purpose:

Very briefly, this is a research seminar. The primary purpose is to present tools and techniques and inspiration aimed directly at moving the participants towards research projects and original innovations.

In a bit more detail, this seminar will explore various aspects of geometric analysis. By geometric analysis I mean geometric measure theory along with other topics from differential geometry, PDE, harmonic analysis, and analysis. Our specific goals are

1) Learning the essential tools we will use over and over again in exploration and creation in geometric analysis. For example, everyone has to understand the basics of Riemannian Geometry, Hausdorff Measure, the Co-area formula, the area formula and so on and so forth.

2) Studying inspirational works that are aligned with research directions we ourselves are taking.

3) Obtaining specific tools needed to solve particular problems we are solving.

We will make frequent use of the books on geometric measure theory by Federer, Morgan, and Simon as well as Evans and Gariepy's "Measure Theory and Fine Properties of Functions".

Notes:

Here you will find links to notes as they are generated.