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 have the opportunity to present either a short talk or a poster at the 2027 Undergraduate Mathematics Symposium, on Friday, April 23 (Room and Time: TBA).
How to Apply
Please complete this form: https://forms.gle/jFTeSiYrXBWoFKYH7
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/
Deadline to submit your application: November 30, 2026, at 2pm.
We welcome applications from all UF undergraduate majors although priority will be given to mathematics majors. Students will only be assigned to projects for which they meet the prerequisites.
Faculty mentors may choose to contact applicants for an interview. The selection process will be completed and participants notified by January 14, 2027.
Spring 2027 Projects
1. Concentration inequalities for random matrices
Faculty mentor: Arnaud Marsiglietti
Description: A random matrix is a matrix whose entries are random variables. Random matrix theory is an important sub-field of probability theory and has applications to many areas of science. The goal of this project is to understand certain statistical properties of random matrices, such as the typical behavior of eigenvalues, when the entries follow Gaussian and more general distributions. Concentration inequalities, which allow a non-asymptotic treatment of random matrices, will serve as the main underlying mathematical tool. Students will become familiar with the language of probability and will gain experience in problem solving.
Prerequisites: Probability theory, linear algebra, and real analysis courses.
Approximate time commitment: 4 hours per week.
2. Do Morse complexes determine isomorphism type?
Faculty mentor: Kevin Knudson
Description: A discrete Morse matching V on a simplicial complex K is a collection of pairs of simplices such that each simplex of K appears in at most one pair, subject to an acyclicity condition. These objects are quite useful for understanding the topology of K; in particular, the pairs allow one to “collapse” the complex K to something smaller while maintaining the homotopy type.
The collection of all such matchings on a given K can be assembled to form another simplicial complex, M(K), called the complex of discrete Morse matchings (or simply the Morse complex for short). Capitelli and Minian proved that if K and L are two complexes with M(K) isomorphic to M(L), then K is isomorphic to L.
There are various subclasses of Morse matchings that one might ask the same question about. In particular, there is a class called strong Morse matchings that can be assembled into a complex SM(K). This complex is usually a proper subcomplex of M(K); it was studied by Knudson and Owens-White. There is also the class of sequential star matchings and the corresponding complex SSM(K). This is a topic of current study by Knudson–Owens-White–Scoville.
The goal of this project is to study the following: if SM(K) is isomorphic to SM(L), does it follow that K is isomorphic to L? What about the same question for SSM(K)?
Prerequisites: Basic topology. Intro to combinatorics might be useful. Linear algebra. No assumption that students know anything about discrete Morse theory.
Approximate time commitment: 3–5 hours per week.
3. Singular perturbations in wave equations
Faculty mentor: Sergei Shabanov
Description: The project is devoted to solutions of a wave equation with coefficients perturbed by singular distributions like the Dirac delta function. The perturbations are regularized by smooth functions that converge in the weak sense to the original distributions. The objective is to investigate convergence of solutions and the regularization independence of the limit solution. Applications will include scattering of electromagnetic waves on dielectric rods and carbon nanotubes.
Prerequisites: MAP 6505; MAP 4341; MAP 4305; linear algebra and multivariable calculus.
Approximate time commitment: 3–5 hours per week.
UGR Archives
Questions?
Email Konstantina Christodoulopoulou (kchristod@ufl.edu) or Sara Pollock (s.pollock@ufl.edu).