2007 Summer REU Program

Subject to final approval from the National Science Foundation, the University of Georgia announces an REU program which will run two summer student research groups of 6-8 students in each of the years 2007, 2008, and 2009. The program will admit students from across the country for a fast-paced and challenging research experience working closely with our mathematics faculty. Students will work closely with UGA faculty and graduate students on a problem of current interest in mathematics research. The REU program is linked to our well-regarded graduate program in mathematics, and students accepted into the REU program will be advised on their preparations for graduate study.

The 2007 REU program will run from June 4 to July 25 at the University of Georgia. Students will be offered stipends of $2800 plus housing and meal plan or $3500 without housing and meal plan for the entire program. Course credit is also available. "Following NSF rules, students must be U.S. citizens or permanent residents to receive REU stipends."

The topics for this year are:

Geometric Probability -- group leader Dr. Joseph H.G. Fu

The first problem in geometric probability is the famous Buffon needle problem: what is the probability that a needle, dropped on a plane ruled by parallel lines an inch apart, crosses one of the lines? This is a very special case of the more general question: given two 2-dimensional shapes, what is the average shape of their intersection if one of them is spun around and tossed randomly onto the other? The same question can be asked for higher dimensional shapes, and if one applies certain measurements, called valuations, to the shape of the intersection, there is a very satisying answer in the form of the "kinematic formulas". It is known that the same kind of answer must exist even if the spinning is restricted to a subgroup of the full rotation group, but the actual formulas remain a mystery! These questions can be asked for finite group actions on finite sets as well. The kinematic formulas turn out to be a repackaged form of a natural multiplication on the set of valuations. The resulting algebra is poorly understood except in the simplest case, but seems to have a lot of combinatorial structure. We will study it in some finite cases and in the geometric case of the unitary group, with lectures and detours to fill in background as needed.

Energies for Plane Curves -- group leader Dr. Jason Cantarella

Suppose that a curve has a negative charge attached to every point. The repulsion of these charges drives nearby sections of the curve away from each other, leading the curve to a (locally) minimal energy configuration. For knotted curves, these minimum energy knots provide "standard" ways to draw the knot. For unknotted curves, these energies provide a way to simplify the knot. This group will work on some new projects concerning the behavior of these energy functionals for plane curves.

For most of these functionals, the curve of minimal energy is the circle. We will be interested in determining whether these functionals have critical configurations other than the circle, and working on extending our results on the circle to new kinds of energy functionals. In the process, we'll learn quite a bit about geometric inequalities in the plane. The group requires a good background in multivariable calculus. More advanced courses covering topics like the calculus of variations would be welcome, but are not required. This group is an instance of the http://ada.math.uga.edu/research/researchgroup/ UGA VIGRE Geometry Group.

Application materials will be due on April 1, 2007 including a transcript, a statement on why you are interested in each project, and two letters of recommendation from faculty. Recommendation letters may be e-mailed directly to Michele Lott, michele@math.uga.edu. Decisions will be announced before April 15. Please download the application form <here> and send application materials to

UGA REU Program
Attn: Michele Lott
UGA Math Department
Boyd GSRC
Athens, GA 30602

Further inquiries can be directed to Michele Lott or to the group leaders directly.

Past UGA REUs