Abstract: Twisted supergravities, as conjectured by Costello and Li, provide a promising approach in the construction of holomorphic and hence controlled sectors of string theory. In this talk, we present our recent progress towards a proof of the conjecture generalised to arbitrary flux backgrounds. We first review our construction of the BV theory of D=10, N=1 supergravity using the framework of generalised geometry. Using this framework, we present our 'Courant Contact Model' as the conjectural result of the twist in arbitrary flux backgrounds. The model is built from the data of a twist of supergravity and can be understood as an analogue of Kodaira-Spencer theory in generalised geometry. We finally show how this recovers the Costello-Li conjecture on Calabi-Yau five-folds.

This talk is based on joint work with Fridrich Valach, Charles Strickland-Constable and Ingmar Saberi (arxiv: 2602.0465, 2501.18008, and 2604.25803).

Abstract: Diffusion type probles arise in a wide range of applications, yet their numerical solution is often constrained by stability and accuracy requirements associated with time-stepping schemes. This presentation explodes the numerical solution of diffusion type problems using the Laplace Transform Finite Difference Method (LTFDM), a hybrid approach in which the governing partial differential equation is transformed into the Laplace domain with respect to time, while spatial derivatives are discretised using finite differences. By eliminating explicit time discretisation, LTFDM removes traditional time-step restrictions and allows the solution to be evaluated independently at any desired time through numerical Laplace inversion. The formulation of LTFDM for linear and nonlinear diffusion probles is outlined, and its performance is demonstrated through representative one-dimensional examples.

Building on this framework, the presentation concludes by outlining future work involvinf the Laplace Transform Radial Basis Function (LTRBF) approach. In the LTRBF finite difference spatial discretisation is replaced with mesh free radial basis function interpolation, this extension aims to accuracy, and svalability to higher-dimensional diffusion problems. The combination of Lapalce-based time treatment with RBF spatial appcoximation offers a promising route towards robust and efficient solvers for complex diffusion-type equations.

Abstract: A computer, in order to perform a given computation, requires a certain amount of space (memory) and a certain amount of time (runtime). This leaves certain computations beyond reach due to technological limits on processing speed and memory density. Some computations, such as the halting problem, are not possible even in principle. However, curved spacetimes and exotic fields appear to provide avenues to accelerate computation, for instance by exploiting time dilation. Impossible computations seemingly become tractable, butting up against intuition. However, we show that such schemes are consistently thwarted by physical effects from quantum gravity (including swampland conjectures) and quantum field theory in curved space. More precisely, we show that an observer and a computer able to withstand energy scales up to order 𝐸 can, by using relativistic effects, accelerate computation at a rate of at most O(1)𝐸 e‐folds per unit time in natural units: (ln⁡ 𝛼)∕𝜏≲𝐸. The Bekenstein bound for entropy can then be understood as the space (memory) analogue to (run)time: if a computer of length scale 𝐷, operating at energies up to order 𝐸, has access to 𝑁 different memory states, then (ln⁡ 𝑁)/𝐷≲𝐸. Based on joint work 2604.00182 with Leron Borsten.

Abstract: The squared amplitude has many interesting physical applications as well as mathematical structures. In this talk, I will briefly review some recent progress on the combinatorial structures of squared amplitudes. In both four-dimensional super Yang-Mills(SYM) and three-dimensional Aharony–Bergman–Jafferis–Maldacena(ABJM) theory, squared amplitudes exhibit a remarkable hidden permutation symmetry that treats loops and external legs on equal footing, leading to similar graphical representation.

Abstract: In recent years a new type of way to relate different field theories has emerged. It goes by various names including 'defects', or 'interface'. In this talk I will report on ongoing work with Nivedita to build foundations for these relations between field theories in the Atiyah-Segal/Stolz-Teichner framework (based on manifolds and their bordisms). This requires various tools from the homotopy theory of generalised notions of smooth spaces, which I am hoping to sketch.

Abstract: The lottery-ball for generating conference names, which has long featured such respectable words as "geometry", "physics", "strings" and "amplitudes", has recently seen the entrance of a young new contender: "higher structures". I will explain (one perspective on) what this is all about, using as an example my work on compactly supported higher bundles with connection. I will use these to describe a picture of something called Poincaré-Pontryagin duality, with applications-in-progress to higher symmetries in certain field theories.

Abstract: In this talk I will be talking about a recent (and my first!) paper. The paper builds on a perspective developed by Hisham Sati and Urs Schreiber which formulates (flux) charge quantization using (real) rational homotopy theory. In doing this they construct a "classifying space of the theory" and in this paper we try to understand what the topology of this space tells us. In particular, we find a nice interpretation of its homotopy and homology groups respectively as defect charges and generalized symmetries. We then study some theories explicitly and reproduce both known generalized symmetries as well as some that have not appeared in the literature. Additionally, we find that this formulation puts constraints on the theories one can write and, conversely, use swampland conjectures to put constraints on the possible classifying spaces for gravity theories.