CURE: Collaborative Undergraduate Research Experience
CURE is an intense 8-week summer research program primarily aimed at mathematics majors. Each summer, the program involves about 4 undergraduate students, one faculty research advisor (Prof. Kemp in 2017) and one graduate student research mentor (Eric Lybrand in 2017). The goals of the program are to:
Participants will be paid a stipend of $4,000 USD. They will be expected to be working (together as a group) with their mentors on weekdays during the program.
2016 Project Description
The topic of this year's CURE project is the eigenvalues of random band matrices. The eigenvalues of symmetric matrices with random
independent entries are, by now, quite well-understood. When the entries are correlated, only very special cases are well-understood. Our goals will be to look at several ensembles
of such matrices that have not been completely solved to date; particularly when the bands (sub- and super-diagonals) are independent from each other, but the entries along each band are correlated. We will study such matrices
on two fronts: computationally and theoretically. We will develop software (in Matlab) to carefully plot good approximations of the distribution of eigenvalues on different scales, and we will use
these plots to give insights into what might be proved about these eigenvalue distributions for large matrices.
Interested students should have taken (the equivalent of) UCSD's Math 180A (probability theory); other courses that are useful but perhaps not essential to have taken are Math 140AB (real analysis), Math 154 or Math 184 (combinatorics), and Math 102A/103 (linear algebra). Some programming experience is also a great benefit. There is no U.S. citizenship/residency requirement. The deadline for application to the 2017 program is Friday, June 2, 2017. Please send the following, by e-mail, to Prof. Kemp.
These materials will be evaluated immediately following the application deadline, and successful applicants will be notified by June 9, 2017.