16th Annual Cantrell Lectures

April 5, 6, 7, 2010

"Singularities in Geometry"

Professor Tobias Colding

Massachusetts Institute of Techonology

Monday, April 5, 2010
Room 102 Miller Learning Center
3:30pm

Curve shortening flow and Mean Curvature flow

Abstract: Mean Curvature Flow is the oldest of the geometric flows (Ricci flow being another example of a geometric flow).  It originates in material science where it has been studied at least since the 1940s.  It is an example of an evolution equation where a surface (or hyper-surface) moves in the direction where the area locally decreases the fastest.  The key problem for any geometric evolution equation is to understand the singularities that the flow goes through.  I will survey some of the results that we know about curve shortening flow and mean curvature flow and discuss what we would like like to know.

*Refreshments will be served preceding lecture outside of Room 102.

A banquet honoring Professor Tobias Colding will be held on Monday, April 5, 2010, 6:00pm at The National restaurant. The seating may be limited, so we ask you to pre-register no later than March 31, 2010.

Tuesday, April 6, 2010
Room 328, Boyd Graduate Studies Bldg.
3:30pm

Minimal surfaces - the birth place of calculus of variations

Abstract: Surfaces that locally minimize area have been extensively used to model physical phenomena, including soap films, black holes, compound polymers, protein folding, etc. The mathematical field dates to the 1740s and Euler and Lagrange, but has recently become an area of intense mathematical and scientific study, specifically in the areas of molecular engineering, materials science, and nanotechnology because of their many anticipated applications.  I will survey some of the recent results of about embedded (ie, without self-intersections) minimal surfaces.

Refreshments will be served preceding lecture in Room 409 Boyd.

Wednesday, April 7, 2010
Room 328 Boyd Graduate Studies Bldg.
3:30pm

Regularity theory

Abstract: I will discuss some of my favorite problems in regularity theory from regularity theory for minimal surfaces, Einstein metrics, and to  curvature flows and will discuss some of the basic techniques to deal with singularities.

Refreshments will be served preceding lecture in Room 409 Boyd.

For additional information about the 2010 Cantrell lecture series please contact any of the following:

Sa'ar Hersonsky, saarh at math dot uga dot edu
Roy Smith, roy at math dot uga dot edu
Julie McEver, julie at math dot uga dot edu