REU Site: Fractals and Stochastics at UConn

University Of Connecticut, Storrs CT

Investigators

Abstract

The REU site will introduce approximately 10 undergraduate students each year to mathematical research by involving them in intensive 10-week research projects that advance knowledge in various areas of mathematics by producing publishable results, conference talks and posters. In addition to research experience, students will practice writing and presenting mathematical work, learn to use software tools for both mathematics research and publication, receive guidance on how to apply to graduate school, and encounter a broad range of mathematical topics through a seminar series. Students will be drawn primarily from non-PhD granting institutions and recruitment will emphasize under-represented groups in the mathematical sciences, including women and minorities. 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 primarily be in aspects of the analysis of fractals and disordered spaces (fractal differential equations, spectral decimation methods), stochastic analysis (ergodic properties of random differential and difference equations, Lyapunov exponents), geometric analysis (geometric properties of random walks on the discrete Heisenberg group and Schreier graphs associated to self-similar groups, functional inequalities, geometry of non-Euclidean structures in Laplacian coordinates). Most projects will involve detailed study of important examples that can be initiated with minimal prerequisites but for which the results are expected to illuminate some larger part of the theory. The projects have substantial connections to other areas of science; for example, the stochastics projects are related to problems in mathematical physics, Laplacian eigencoordinates and their variants are widely used in machine learning, and fractals and disordered media can be used to model physical structures studied in areas from geology (distribution of oil or water in porous rock) to computer science and neurobiology (structure of neural networks). Further details about the program are available at https://mathreu.uconn.edu 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.