National Science Foundation

Research Experiences for Undergraduates (REU)

2019 Projects

Blessing Emerenini: Mathemataical Biology. Dr. Emerenini is a researcher in mathematical biology with particular applications in ecology, infectious diseases and agriculture using the tools of differential equations, control theory, numerical analysis and simulations. Dr. Emerenini's project this summer is on investigating persistence and extinction in a superspreading event using a stochastic model. Superspreading events have been reported for many infectious disease outbreaks such as Ebola and Tuberculosis. In order to control superspreading in an epidemic, there is need to understand the disease persistence and extinction. Her project is in mathematical biology and will involve model formulation and computer simulations to investigate persistence and extinction in a superspreading event.

Clayton Petsche: Dynamics of Polynomial Maps Dr. Petsche is a number theorist with a primary focus on the area of arithmetic dynamical systems. Dr. Petsche proposes an exploration of topics in algebraic dynamical systems in several variables over p-adic and other non-Archiedean fields. Possible projects include:
  1. Find a new, dynamical proof of the non-Archimedean Perron-Frobenius theorem established in the 2015 OSU REU, based on fixed-point theory. Does such an approach have further non-Archimedean applications in parallel with the real setting?
  2. Classify the dynamics of non-Archimedean Henon maps in residue characteristic 2, the excluded case in the 2016 OSU REU.
  3. Perform new and interesting calculations of dynamical invariants, such as entropy, Hausdorff dimension, and the growth rate of periodic points, in the context of p-adic plane automorphisms.
Mike Rosulek: Secure Computation Dr. Rosulek is a researcher in cryptography, with specific interest in secure computation protocols. A secure computation protocol allows n parties, each of which has a private input, to learn some agreed-upon function of their inputs, while learning nothing else. Dr. Rosulek's project is to study problems related to secure multi-party computation (MPC), which is a cryptographic technique that allows computing on private data. More specifically, if several parties have private inputs x1, x2, ..., x_n, then they can interactively compute some function f(x1,...,x_n) of those inputs so that they learn this output but learn no other intermediate values of this computation (including the inputs).

Holly Swisher: Partitions and Modular Forms Dr. Swisher's research is inspired by the work of Ramanujan with a primary focus on questions related to integer partitions and modularity. Notably, the subjects of mock modularity and most recently quantum modularity have gained a lot of current interest. In 2015, her REU students studied quantum modularity properties of a class of mock modular forms related to certain theta functions. Dr. Swisher's proposed project is to investigate quantum modularity properties for certain classes of generalized partition rank generating functions which have a particularly nice hypergeometric shape.

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