CURE: Collaborative Undergraduate Research Experience

Administrative Information

Application Deadline: June 1, 2018
Start Date: Monday, July 5, 2018
End Date: Friday, August 29, 2018
Location: AP&M, UCSD   Map

Advisor:    Todd Kemp


Program Description

CURE is an intense 8-week summer research program primarily aimed at mathematics majors. The program involves 4-5 undergraduate students, a faculty research advisor (Dr. Ian Charlesworth in 2018), one graduate student research mentor, along with the program advisor Prof. Todd Kemp. 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 are paid a stipend of $4,000 USD, in two monthly installments. They are expected to be working (together as a group) with their mentors on weekdays during the program.

2018 Project Description

The topic of this year's CURE project is bi-free probability theory. Free probability is a large research area overlapping analysis, probability, and combinatorics. It can be viewed as the large-dimension limit of random matrix theory, and has provided important, robust tools for answering questions in a wide variety of pure and applied fields: from operator algebras to wireless communication; from representation theory to string theory. Bi-free probability is a more recent invention (about 5 years old) that introduces a "two faced" structure into the theory. There are still many questions in the underlying combinatorial structure of free probability that have yet to be generalized to the bi-free setting; CURE 2018 will be devoted to understanding and extending some of these combinatorial ideas.

Application Procedure

CURE is open to all current full-time UCSD students. Interested students should have taken Math 140AB (real analysis). Other courses that could be useful are Math 180A (probability theory), Math 154 or Math 184 (combinatorics), and Math 102 (linear algebra). Some programming experience is also a great benefit. There is no U.S. citizenship/residency requirement, but you must have legal status to live and work in the U.S. through at least September 1, 2018. The deadline for application to the 2017 program is Friday, June 1, 2018.

Submit your application using this Application Form. You will need to submit:

  • A current cv.
  • An up-to-date academic transcript (official not necessary; a pdf download from the registrar is fine).
  • A list 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).
  • 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 8, 2018.