My research has been in two broad areas namely mathematical biology and disability studies. This talk will touch upon three of my projects in mathematical biology and one project in…
Elliptic integrands are used to model anisotropic energies in variational problems. These energies are employed in a variety of applications, such as crystal structures, capillarity problems and gravitational fields, to…
Experts have long realized the parallels between elliptic and parabolic theory of partial differential equations. It is well known that elliptic theory may be considered a static, or steady-state, version…
Differential games, as an offspring of game theory and optimal control, provide the modeling and analysis of conflict in the context of a dynamical system. Computing Nash equilibria is one…
In this talk, I will discuss two different 'ranking' models: Mallows' ranking model and rank-dependent diffusions. In the first part, I will discuss the rank-dependent diffusions. I will focus on…
Quantized higher Teichmüller theory, as described by Fock and Goncharov, assigns an algebra and its representation to a surface and a Lie group. This assignment is equivariant with respect to…
The cellular cytoskeleton is essential in proper cell function as well as in organism development. These filaments represent the roads along which most protein transport occurs inside cells. I will…
Fusion categories are rich mathematical structures generalizing the representation categories of finite groups. They arise in many areas of mathematics and physics. Most strikingly, they have emerged as models for…
A hypersurface in a Riemannian manifold is called minimal if its mean curvature vanishes identically. Minimal surfaces have fascinated mathematicians since the time of Euler, and tremendous progress has been made in…
This talk will cover two approaches for modeling blood flow in the human body. The first approach describes blood transport in elastic vessels and requires the numerical solution of a nonlinear…
What can we tell about the interior structure of our planet, if we observe the travel time of a large number of earthquakes? This is the time it takes for a seismic…
Many materials are built from a grid of flexible but nearly inextensible rods that behaves as a shell-like structure. Everyday examples range from fabrics made of 1000s of interwoven yarns;…
Pertussis, commonly known as whooping cough, is caused by the bacterial pathogen Bordetella pertussis. Completely susceptible individuals experience severe disease, with the hallmark whooping cough, but those with partial immunity have…
Students often take precalculus or college algebra as a terminal math course, leaving them with the impression that mathematics lacks real meaning. Due to the increasingly interdisciplinary nature of the…
A circle packing is the mathematical name for a collection of circles. I am interested in circle packings with a fixed pattern of tangencies between the circles. Given a tangency…
In this demo, we will discover some interesting properties about symmetry by starting with some special transformation matrices. This talk will be a combination of interactive work with the material…
How could you design a stadium so that a rectangular playing field looks the same size to every spectator? What about for a circular wrestling ring? In this talk, we…
Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in the modeling, simulation,…
Principal component analysis (PCA) is a useful tool when trying to uncover factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model…
Persistent homology is a key method in topological data analysis, a young but rapidly growing field at the intersection of computational geometry and algebraic topology. Persistence is used to describe…