Mathematical Institute (University of Oxford)

In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability, and topological data analysis to study these the dynamics of ERK. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

Tensors are higher dimensional analogues of matrices; they are used to record data with multiple changing variables. Interpreting tensor data requires finding low rank structure, and the structure depends on the application or context. Often tensors of interest define semi-algebraic sets, given by polynomial equations and inequalities. I'll give a characterization of the set of tensors of real rank two, and answer questions about statistical models using probability tensors and semi-algebraic statistics. I will also describe work on learning a path from its three-dimensional signature tensor. This talk is based on joint work with Guido Montúfar, Max Pfeffer, and Bernd Sturmfels.

In this talk, I am going to give an introduction to operator preconditioning as a general and robust strategy to precondition linear systems arising from Galerkin discretization of PDEs or Boundary Integral Equations. Then, in order to illustrate the applicability of this preconditioning technique, I will discuss the simple case of weakly singular and hypersingular integral equations, arising from exterior Dirichlet and Neumann BVPs for the Laplacian in 3D. Finally, I will show how we can also tackle operators with a more difficult structure, like the electric field integral equation (EFIE) on screens, which models the scattering of time-harmonic electromagnetic waves at perfectly conducting bounded infinitely thin objects, like patch antennas in 3D.