Skip to main content
College of Liberal Arts and Sciences University of Florida

Undergraduate Research Program in Mathematics

The UF Undergraduate Research Program in Mathematics supports semester-long, faculty-led research projects for undergraduate students. Participants work individually or in small teams on projects designed and proposed by UF Mathematics faculty.

The program’s main goals are to give undergraduates experience in mathematical research and to help them strengthen their problem-solving, communication, and collaboration skills.

Project structure and meeting schedules are determined by the faculty mentor. Students will enroll in a section of MAT4911: Undergraduate Research in Mathematics under the supervising faculty mentor for 1-3 credits. We anticipate being able to provide a stipend to student participants, depending on available funds.  Participants will be invited to present their work at the Spring 26 Undergraduate Mathematics Research Symposium (tentatively scheduled for April 24, 2026).

How to Apply

We welcome applications from all UF undergraduate majors although priority will be given to mathematics majors.  If you are an undergraduate student at UF interested in participating in the program, please complete this form by December 3:

https://forms.gle/bHBjcNwHqiX6qaY19

Note: To access  the form, you must login to Google forms with your @ufl.edu email: https://cloud.it.ufl.edu/collaboration-tools/g-suite/

Please only apply to projects for which you have met the prerequisites! Faculty mentors may choose to contact applicants for an interview.  The selection process will be completed  and participants notified by the January 14, 2026.

Below you will find the projects open to applications for Spring 2026.

 Spring 26 Projects

Dirac delta-function potentials in the Schroedinger operator

  • Faculty Mentor: Dr. Sergei Shabanov
  • Description: Dirac delta-functions potentials are used to model quantum systems with a short-range and high strength potential. However, either scattering or eigenvalue problems for the Schroedinger operator with such a potential in two or higher dimensions requires a regularization of the delta-function (e.g., a Gaussian regularization).  However all observables, such as the discret spectrum of the operator and the scattering matrix, are singular in the limit when the regularization is removed. To obtain finite results for observables a so-called renormalization of the potential strength is applied, a procedure that is similar to renormalization in quantum field theory. Renormalization depends on a regularization of the delta-function. Only for a very limited class of regularizations (in fact, just for a few) it was proved in two spatial dimensions that the observables are regularization-independent. It has recently been proposed that the delta-function potentials can be used in a non-linear Schroedinger equation to model Bose-Einstein condensations, which is a fundamental phenomenon in modern physics. The key mathematical question of regularization-independence of these non-linear and previous linear models remains unaddressed and becomes even more significant. The ultimate project goal is to investigate this problem in the simplest case of the 2D linear Schroedinger operator and either to prove the assertion for any regularization or construct a counter example. Specifically, no regularizations that break the rotational symmetry have ever been studied in this regard, and a technical goal of the project will be to investigate them.
  • Prerequisites: Linear Algebra (4000-level); PDE (4000-level is sufficient); MAP 6505 (necessary), MAP 6506 (helpful).
  • Approximate hours per week  students are expected to devote to the project: 4-6 hours.

Probabilistic properties of heavy-tailed distributions

  • Faculty Mentor: Dr.  Arnaud Marsiglietti
  • Description: Heavy-tailed distributions in probability theory and statistics form an important class of distributions that appear naturally in many areas of applied science. The goal of this project is to study generic probabilistic properties of heavy-tailed distributions, such as deviation inequalities, moment bounds, and entropic estimates. Students will become familiar with the language of probability and will gain experience in problem solving.
  • Prerequisites: Calculus/intro analysis and probability/statistics courses
  • Approximate hours per week  students are expected to devote to the project:  4 hours

Questions?

Email Konstantina Christodoulopoulou (kchristod@ufl.edu) or Sara Pollock (s.pollock@ufl.edu).