Research

Mathematical methods for single cell sequencing

Rapid progress in genetics and sequencing technologies is producing a flood of data on fundamental biological questions from healthy development to disease progression and treatment. To realize the full potential benefit of the data, we need complementary mathematical and statistical techniques adapted to experimental possibilities. Along the way, the experiments provide continuing inspiration for novel applied mathematics.

Network theory

A key property of networks in a range of physical and computational contexts is the spectrum of eigenvalues of certain associated matrices, especially the graph Laplacian. Controlling that spectrum, which can be done exactly in theory and approximately in practice, enables controlling the behavior of the corresponding network dynamical systems.

Active fluids

In an active fluid, flow is driven by small-scale internal energy input rather than externally imposed forces and pressure gradients. Typical examples include dense suspensions of bacteria, where the swimming bacteria drive the flow, or polymers driven by active motors, as happens inside cells in our bodies. From a scientific point of view, models of active fluids shed light on fundamental questions in biology on the microscale; from an engineering perspective, active driving offers novel avenues for controlling fluid motion.