REU Site: Mathematics REU at UConn

University Of Connecticut, Storrs CT

Investigators

Abstract

The REU site will involve approximately 9 undergraduate students each year in intensive 10-week research projects intended to advance knowledge in various areas of mathematics and mathematical finance by producing publishable results, conference talks and posters. In addition to research experience, the program will give students practice in writing and presenting their work, teach them how to use software for mathematics and expose them to a broad range of mathematical topics through a weekly seminar series, including a workshop on applying to graduate school. Students will be drawn primarily from non-PhD granting institutions, and recruitment will emphasize under-represented groups in the mathematical sciences, including women, minorities and persons who are deaf or hard-of-hearing. A major goal is to contribute to the development of human resources in mathematics and mathematically intensive areas by increasing the likelihood that these students go on to graduate study and/or a career in these fields. Undergraduate research projects will be in several areas, including geometric and functional analysis (functional inequalities on the discrete Heisenberg group), stochastic processes and ergodicity (estimates and asymptotic formulas for Lyapunov exponents of differential and difference equations with small random perturbations), analysis on fractals and disordered spaces (diffusion processes and differential equations on fractal spaces including limit sets of groups), and applications of probability theory in mathematical finance. Many of the specific projects involve investigating basic examples that are expected to illuminate some larger part of the theory. Participants will be working on research projects that have either direct applications, e.g. in finance, or substantial connections to other areas of science; for example a number of the fractals/disordered media projects are about properties of differential equations on sets that can be used to model physical structures like porous media and neural networks, and the stochastics projects are closely linked to problems in mathematical physics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.