Projects are listed by faculty member. Please contact faculty members directly for further information.
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.
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. 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.