Department of Mathematics
University of Georgia
2010 Summer REU Programs

The Department of Mathematics at the University of Georgia announces a REU program for research group of 6-8 students during summer 2010. This 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 with UGA faculty, Post-docs and graduate students on problems of current interest in mathematics research. The REU programs are linked to our well-regarded graduate program in mathematics, and students accepted into the REU program will be counseled on their preparations for graduate study.

The 2010 REU program will run from June 7-July 23. It will be held on the University of Georgia campus in Athens, Georgia. Housing, travel support and a stipend will be provided. A meal plan will be available for purchase during the program. Course credit is also available. "Following NSF rules, students must be U.S. citizens or permanent residents to receive REU stipends." Students from minorities and/or disadvantaged groups are especially encouraged to apply.

The topic for this year is:

Structure and Randomness: An Invitation to Arithmetic Combinatorics
(June 7 – July 23)
Group Leaders –Neil Lyall and Mariah Hamel

Arithmetic combinatorics arose out of the interplay between number theory, combinatorics, ergodic theory and harmonic analysis. Problems in this exciting and fast growing area have a broad appeal and have invited the attention of a diverse group of mathematicians. A famous example is Szemerédi's theorem, stating that if a set contains a "positive proportion" of the natural numbers, then it must contain arbitrary long arithmetic progressions. Although several different proofs of this deep theorem are now known, each relies crucially on a fundamental dichotomy between structure and randomness, which roughly speaking allows any object to be decomposed into a structured component and a random component. One striking recent application of this dichotomy is the result of Green and Tao, establishing that the prime numbers contain arbitrarily long arithmetic progressions despite containing only a "zero proportion" of the integers.

The aim of this REU will be to gain an understanding of some of the basic ideas and arguments in arithmetic combinatorics (through exercises, problems, and studying articles) with an eye toward some related open problems. There will be a minimal amount of formal teaching, and a lot of easy, not so easy, and very difficult problems for the participant to sink their teeth into.

The topics that we propose to investigate should be accessible to students with no prior exposure to the field, although some previous exposure to either combinatorics, graph theory, or real analysis would be desirable. Applicants should have had at least two upper division math courses which involve reading and writing proofs.

Application materials will be due on April 1, 2010 including a transcript, a statement on why you are interested in the project, and two letters of recommendation from faculty. Decisions will be announced by April 15, 2010. Please download the application form <here> and send application materials to:

UGA REU Program
UGA Math Department
Boyd GSRC
Athens, GA 30602

Further inquiries can be directed to reu@math.uga.edu,
Neil Lyall: lyall@math.uga.edu or Mariah Hamel: mhamel@math.uga.edu .