CURE: Collaborative Undergraduate Research Experience


Administrative Information

Application Deadline: June 2, 2017
Start Date: Wednesday, July 17, 2017
End Date: Friday, September 8, 2017
Location: AP&M, UCSD   Map

Advisor:    Todd Kemp
E-mail:      tkemp@math.ucsd.edu

 

Program Description

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:

  • explore a topic in research-level mathematics,
  • promote collaborative work in the next generation of mathematicians,
  • encourage graduate study in mathematics, and
  • promote diversity in mathematics.

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.

Application Procedure

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.

  • A current cv.
  • An up-to-date academic transcript (not necessary if you are a UCSD student).
  • A list and brief description of all upper-division mathematics courses you have taken, in addition to any courses or training in related computational fields (e.g. computer science and computer engineering, physics).
  • A one page sample of mathematical writing. This can be on a topic of mathematics research you have worked on in the past, or it can be an exposition of a favorite theorem you've learned in (or out of) your course work. The goal is to demonstrate your enthusiasm for, and ability to communicate, rigorous mathematical ideas.

These materials will be evaluated immediately following the application deadline, and successful applicants will be notified by June 9, 2017.