current student(s)

Name    Project Title
L. Sadergaski    Representations of Dihedral and Rotation Groups

potential projects

Pattern Formation in Animal Coat Patterns
Morphogenesis is the biological process by which form and structure is created during embryonic development. How are pigment cells determined and distributed through the skin when a mammal develops? How does this process determine the types of patterns in animal coat patterns, such as zebra stripes and cheetah spots? We can investigate this process through the following system of partial differential equations, known as the reaction-diffusion equations: \[\begin{aligned}u_t &= \Delta u + \gamma\left[a-u-\frac{\rho u v}{1+u+Ku^2}\right],\\v_t &= d\Delta v + \gamma\left[\alpha(b-v)-\frac{\rho u v}{1+u+Ku^2}\right].\end{aligned}\]

Nonlinear Mass-Action and Stochasticity in SIR Models
The standard SIR model is used to study how an infectious disease is spread through a healthy population. The model has many shortcomings. We study differences in the populations in a systematic manner through the following model: \[\begin{aligned}S' &= -\beta S^xI^y\\I' &= \beta S^xI^y - \alpha S^mI^n\\R' &= \alpha S^mI^n\end{aligned}\]

previous students

Name    Project Title    Year
A. Prudhom    Multiplication Operators Between \(\mathcal{L}^{(p)}\) Spaces on a Tree    2012-2013
T. Xiong    The Contagiousness of Rumors    2012
C. Jens    Surviving an Outbreak of Zombiism    2010-2011