National Science Foundation

Research Experiences for Undergraduates (REU)

2017 Projects

In 2017, the following faculty members will direct student projects:

Nathan Gibson, of the Mathematics Department, is a researcher in the areas of Numerical Analysis and Applied Mathematics. His research interests include numerical methods for differential equations and uncertainty quantification. This summer's project will involve dynamic (time-varying) systems whose parameters may have statistical variation (either from uncertain measurements or from a heterogeneous domain). Numerical methods for incorporating this uncertainty are similar to spatial discretizations, namely finite difference, finite element, or spectral based. The project will explore accuracy and efficiency for one or more of these approaches for particular applications.

See the proceedings from 2008-2010 for previous projects directed by Professor Gibson.

Ren Guo, of the Mathematics Department, is a researcher in the area of geometry and topology. The project proposed by Guo for the coming summer is to study classical geometry in Euclidean space, hyperbolic space, and spherical space. One of the goals is to generalize results in Euclidean geometry or convex geometry in Euclidean space into hyperbolic and spherical geometry. These include identities and inequalities involving lengths, angles, area or volume of geometric objects. Another goal is, via comparing the results in the three geometries, to investigate the difference and unification of the three geometries. Participants of this project may choose to focus on some specific questions or conjectures depending on their backgrounds and interests. Participants will be expected to have basic knowledge in calculus and linear algebra.

See the proceedings from 2016 for previous projects directed by Professor Guo.

Yevgeniy Kovchegov, of the Mathematics Department specializes in applied probability and stochastic processes. Kovchegov also works in the field of quantum computing. He is currently researching coalescent processes, which are used in biology and physics. The projects for this coming summer is to consider some generalized classes of coalescent processes and examine certain self-similarity properties and gelation (appearance of a giant cluster). Skills needed are basic probability and differential equations.

See the proceedings from 2008-2013, 2015-2016 for previous projects directed by Professor Kovchegov.

Juan Restrepo, of the Mathematics Department specializes in geophysical fluid dynamics, scientific computing, and uncertainty quantification. The project for this summer is to develop a model for the spread of an imperfect idea through a heterogeneous population. Like all imperfect ideas or rumors, these will have varying degrees of factual information, and further, the veracity can change in time. There are two parts to this project: one part consists of building a model for the spread of a rumor in a time dependent and spatially extended network of expert and non-expert interacting agents, the second one is to construct a Bayesian estimator that uses the model and data to estimate how and when a rumor percolates through the network, while at the same time, tracking its trustworthy information content. This project is in collaboration with Dr. Matt Sottile from Sailfan Research, Inc. Portland OR.

Mike Rosulek is a cryptographer in the School of Electrical Engineering and Computer Science. He proposes research projects related to memory-hard functions (MHFs), which are used as password hashing functions and as proofs-of-work in blockchains. In both of these realms, a major concern is whether the economic cost of evaluating these functions can be reduced by building special-purpose hardware. The design goal of an MHF is to require a sustained and significant amount of *memory* to evaluate, since the economic cost of memory (unlike processing speed) is roughly the same across all hardware architectures. In this project, we will investigate theoretical aspects of MHFs, with the goal of identifying provably optimal MHF constructions. Prospective students should have a strong background in combinatorics & graph theory.

See the proceedings from 2015 for previous projects directed by Professor Rosulek.

In general, the proceedings from the past few years will give an idea of the variety and general levels of the projects.