L2

Symmetry Topological Field Theories (SymTFTs) are topological field theories that encode the symmetry structure of global symmetries in terms of a theory in one higher dimension. While SymTFTs for internal (global) symmetries have been highly successful in characterizing symmetry aspects in the last few years, a corresponding framework for spacetime symmetries remains unexplored. We propose an extension of the SymTFT framework to include spacetime symmetries. In particular, we propose a SymTFT for the conformal symmetry in various spacetime dimensions. We demonstrate that certain BF-type theories, closely related to topological gravity theories, possess the correct topological operator content and boundary conditions to realize the conformal algebra of conformal field theories living on boundaries. As an application, we show how effective theories with spontaneously broken conformal symmetry can be derived from the SymTFT, and we elucidate how conformal anomalies can be reproduced in the presence of even-dimensional boundaries.
 

One of the great powers of global symmetry is its ability to constrain the possible phases of many-body quantum systems. In this talk, we will present a symmetry that enforces every symmetric model to be in a phase with a Fermi surface. This constraint is entirely non-perturbative and a strong form of symmetry-enforced gaplessness. We construct this symmetry in fermionic quantum lattice models on a $d$-dimensional Bravais lattice, and it is generated by a U(1) fermion-number symmetry and Majorana translation symmetry. The resulting symmetry group is an infinite-dimensional non-abelian Lie group closely related to the Onsager algebra. We will comment on the topology of these symmetry-enforced Fermi surfaces and the UV symmetry's relation to the IR LU(1) symmetry of ersatz Fermi liquids. (This talk is based on ongoing work with Shu-Heng Shao and Luke Kim.)

I will explain how the irreversibility of the renormalization group together with anomalies, including anomalies in the space of coupling constants, can be used to constrain the IR phases of defects in familiar quantum field theories. As an example, I will use these techniques to provide evidence for a conjectural "spin-flux duality" which describes how certain line operators are mapped across particle/vortex duality in 2+1d.

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.