First MTP Research Day 19/09/2025

Abstract: I loves Killing things, and so should you. I will explain three ways (worldvolume, geodesic, bulk theory) in which Killing things are symmetries of particles and strings. Based on ongoing joint work with Mateo Galdeano, who loves Killing things too.

Abstract: What is the difference between "agents" - things that we perceive as having goals and taking actions in order to achieve them - and other kinds of physical system? An answer to this was proposed by the philosopher Daniel Dennett: we can consider a system to be an agent if we can make good predictions of its behaviour by treating it 'as if' it is an agent. This sounds tautological but it isn't, since some systems (e.g. humans, robots) are much better predicted by taking this 'intentional stance' than others. I'll present a thread of work that tries to make this idea mathematical, as well as combining it with ideas from control theory, Bayesian inference and category theory. The work has potential implications for artificial intelligence as well as cognitive science.

Abstract: The heterotic G2 system describes compactifications of heterotic supergravity on a 7-dimensional manifold preserving N=1 supersymmetry. Solutions to the system involve interesting constructions in geometry such as G2-structures and G2-instantons, but they are challenging to obtain! In this talk I will give an overview of the heterotic G2 system and briefly present some solutions that I constructed together with Leander Stecker.

Abstract: This talk will not really be about a specific result; rather, it will represent an effort to hold on to some inchoate pieces of general philosophy that have been visible in many or all of the recent projects I've thought about, and to fuse them together into some kind of coherent framework.

The context is that of "supergravity theories," which are particular examples of physical theories including both fermions and gravitational fields. Gravity is distinguished by two properties: (1) it describes the deformation problem of a natural geometric structure on manifolds, in this case an Einstein metric, which makes no reference to other background structures ("general covariance"); (2) it is captured by a variational principle. One is tempted to ask whether (1) can be extended to include the fermions; different Ansätze are available in the literature, all of which seem justified to a greater or lesser extent. I hope to be able to say something about fitting them together.

Abstract: Wall's D(2) problem is among the most significant problems left unsolved in low-dimensional topology. I will provide a brief overview of this problem before discussing the extent to which it can be solved for complexes whose fundamental group is a metacyclic group. A key object in this study will be the syzygy modules of the trivial Z[G] module Z.

Abstract: The scattering amplitudes of several theories have been shown to manifest combinatorial properties which can be efficiently encoded into geometrical pictures called positive geometries. So far, this framework has generated new perspectives both in the efficient computation of scattering amplitudes and in adjacent mathematical fields. 

I will give a short introduction to the definitions of positive geometries and some of their features. Next, I will present a physical application to scalar theories, the kinematic associahedron and, finally, a family of important positive geometries, the arrangements of hyperplanes. 

Abstract: Cosmological correlators are the observables of interest in cosmology, encoding properties of the initial conditions of the universe. Recent advances have seen the application of amplitudes techniques to the computation of these correlators, nominally differential equations.

I will present a geometrical approach to the problem through logarithmic differential forms, that will allow us to generate canonical differential equations from combinatorial properties of graphs.

Abstract: Vertex algebras are a mathematical formalism capturing physical intuitions about chiral conformal field theories in complex dimension one; they appear ubiquitously in quantum integrable models and representation theory.

For various motivations, one would like to go beyond complex dimension one to higher dimensions. Chiral algebras/factorization algebras provide a promising framework for doing that. 

I'll begin a quick overview of my own big-picture motivation, which come from quantum integrable Gaudin models (in fancy language, the geometric Langlands correspondence). 

Then I'll try to give a flavour of my ongoing work, joint with Zhengping Gui and Laura Felder, on constructing higher dimensional chiral algebras.