L2

Einstein’s equations are difficult to solve and if you want to compute something in holography knowing an explicit metric seems to be essential. Or is it? For some theories, observables, such as on-shell actions and free energies, are determined solely in terms of topological data, and an explicit metric is not needed. One of the key tools that has recently been used for this programme is equivariant localization, which gives a method of computing integrals on spaces with a symmetry. In this talk I will give a pedestrian introduction to equivariant localization before showing how it can be used to compute the on-shell action of 6d Romans Gauged supergravity. 
 

I will outline some recent progress in identifying realistic models of particle physics in heterotic string theory, supported by several mathematical and computational advancements which include: analytic expressions for bundle valued cohomology dimensions on complex projective varieties, heuristic methods of discrete optimisation such as reinforcement learning and genetic algorithms, as well as efficient neural-network approaches for the computation of Ricci-flat metrics on Calabi-Yau manifolds, hermitian Yang-Mills connections on holomorphic vector bundles and bundle valued harmonic forms. I will present a proof of concept computation of quark masses in a string model that recovers the exact standard model spectrum and discuss several other models that can accommodate the entire range of flavour parameters observed in the standard model. 

Recently, much attention has been paid to the intersection between coarse geometry and graph theory, giving rise to the fresh, exciting new field aptly known as ‘coarse graph theory’. One aspect of this area is the study of so-called ‘fat minors’, a large-scale analogue of the usual idea of a graph minor.

In this talk, I will introduce this area and motivate some interesting questions and conjectures. I will then sketch a proof that a finitely presented group is either virtually planar or contains arbitrarily ‘fat’ copies of every finite graph.

No prior knowledge or passion for graph theory will be assumed in this talk.

During the talk I will describe my research on host-pathogen interactions during lung infections. Various modelling approaches have been used, including a hybrid multiscale individual-based model that we have developed, which simulates pulmonary infection spread, immune response and treatment within in a section of human lung. The model contains discrete agents which model the spatio-temporal interactions (migration, binding, killing etc.) of the pathogen and immune cells. Cytokine and oxygen dynamics are also included, as well as Pharmacokinetic/Pharmacodynamic models, which are incorporated via PDEs. I will also describe ongoing work to develop a continuum model, comparing the spatial dynamics resulting from these different modelling approaches.  I will focus in the most part on two infectious diseases: Tuberculosis and COVID-19.

The beautiful displays exhibited by fish schools and bird flocks have long fascinated scientists, but the role of their complex behavior remains largely unknown. In particular, the influence of hydrodynamic interactions on schooling and flocking has been the subject of debate in the scientific literature. I will present a model for flapping wings that interact hydrodynamically in an inviscid fluid, wherein each wing is represented as a plate that executes a prescribed time-periodic kinematics. The model generalizes and extends thin-airfoil theory by assuming that the flapping amplitude is small, and permits consideration of multiple wings through the use of conformal maps and multiply-connected function theory. We find that the model predictions agree well with experimental data on freely-translating, flapping wings in a water tank. The results are then used to motivate a reduced-order model for the temporally nonlocal interactions between schooling wings, which consists of a system of nonlinear delay-differential equations. We obtain a PDE as the mean-field limit of these equations, which we find supports traveling wave solutions. Generally, our results indicate how hydrodynamics may mediate schooling and flocking behavior in biological contexts.