I am interested in understanding certain extremal configurations in the discrete cube using techniques in optimization, such as linear and semi-definite programming. This approach was initiated by Francois Delsarte in his work on error-correcting codes, in which he showed that a good code provides a solution to a certain linear programming problem. Understanding the linear program leads to a better understanding of codes. The questions I want to address are somewhat different but essentially of the same flavor.

I would be happy to work with a student with a good mathematical and computer science background, who is interested in combinatorics and optimization. The student will help in solving small scale optimization problems using appropriate mathematical software (Mathematica or MATLAB) and in interpreting the solutions. I might also need some help with the literature. The student might be asked to read and scan some papers or book chapters on relevant topics.

The student will get acquainted with two very nice research topics in applied mathematics and the connections between these topics, and also obtain some experience in using mathematical software.