# Possible Student Research Topics

## Possible Topics for Student Research Projects in Mathematics

Projects are listed by faculty member. Each faculty member on this list is willing to take on students as February 2016. Please contact faculty members directly for further information. (Last updated August 20, 2016)

**Dr. Gaddis:** I work in noncommutative algebra. This is a field where we throw out one of the basic tenants of multiplication (commutativity) and replace it with “rules” for how elements should interact. More specifically, I like to classify these objects and establish order where previously there was chaos. I am excited to work with students who enjoy algebraic manipulations, are interested in applying or learning computational skills in mathematical software (MAPLE, Mathematica, GAP, etc), or who just want to learn a different side to algebra.

**Dr. Gemmer: ** Broadly, my research interests lie in analyzing and developing mathematical models of phenomenon in the physical and biological sciences. As an applied mathematician I find significant professional satisfaction studying “toy” models of systems which can yield concrete insights into phenomena observed in Nature. I am also particularly drawn to problems which not only have interesting and important applications but also have the potential to lead to new and deep mathematics. In my work I have developed expertise in calculus of variations, mathematical modeling, applied analysis, continuum mechanics, asymptotic methods, ordinary and partial differential equations and Riemannian geometry. I would be happy to meet with a student to discuss potential projects. Past projects I have mentored include modeling crowd dynamics, modeling the spread of infectious diseases on adaptive networks, brachistochrone problems in inverse square gravitational fields, rare events in stochastic differential equations, modeling adaptation in predator prey systems, and studying the stability of inverted pendulums, i.e. segues. A list of potential and past projects is available at http://users.wfu.edu/gemmerj/projects.html.

**D****r. Hallam:** I am interested in enumerative combinatorics and algebraic combinatorics. At its core, enumerative combinatorics is the study of counting objects, whereas algebraic combinatorics is the interplay between algebra and combinatorics. In the past, I have studied partial ordered sets and symmetric functions, but I am willing to work on something else in enumerative or algebraic combinatorics.

**Dr. Hepler: **I am interested in statistical modeling for data that are dependent in space and/or time. I am also interested in Bayesian modeling and computation. Potential areas of application for student projects are in the environmental and ecological sciences and in public health/epidemiology. I am also open to other areas that students may be interested in.

**Dr. Jiang: **1. Network models of infectious disease: try to investigate the difference between A Markov chain model and a deterministic model. Keywords: Markov chain, rate of eradication, network model, dynamical systems. 2. Multifractal analysis of time series. Keyword: Holder exponents, Wavelet coefficients, Hausdorff dimension

**Dr. Norris: **I would be very interested in working with a dedicated undergraduate or masters student in statistical methodology or applied statistics.

**Dr. Raynor: **I’m open to working on any topic in the general areas of analysis, differential equations, and differential geometry. Some areas on which I’ve worked with students before are traffic modeling, free boundary problems, DNA solitary wave modeling, fractals, and ranking theory.

**Dr. Rouse: ** Rather than indicate a specific project, I prefer to decide on a project after talking with a student about their interests and background. That said, all the projects I am likely to suggest are in number theory.