Triangle Seminars

Abstract:
Formalization of mathematics in computer theorem provers such as Lean is an area which has seen a huge growth in popularity in this decade. AI tools which can write Lean code are now appearing, and people are using these tools to verify LLM output. I'll talk about motivations for the formalization of mathematics, bottlenecks, and the role which AI has to play in the future of this area.

This is the first lecture in the new AI for Mathematical Sciences (AIMS) seminar series: https://lims.ac.uk/events/aims/
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Abstract:
GR, while one of the most successful and well-tested theories to date, is expected to receive corrections at high energies—through higher-curvature terms, additional degrees of freedom, or both. Given the vast landscape of possible extensions, how can we test them in a systematic way?

I will present a general framework for interpreting deviations in gravitational wave data, focusing on the inspiral regime probed by LIGO. The key idea is that genuine beyond-GR effects exhibit characteristic mass scalings, determined by the curvature order and field content of the underlying theory. Using techniques from Post-Newtonian Effective Field Theory (PN-EFT), we construct a dictionary between such corrections and their imprint on the waveform. This allows broad classes of higher-curvature modifications to be identified or constrained directly from data, without relying on specific models. The talk will be based on arXiv:2507.17143.

Abstract:
The problem of scale separation - i.e. whether String Theory admits AdS vacua where the size of the extra dimensions can be made parametrically smaller than the AdS radius - is an outstanding problem in string phenomenology. Moreover, it is also a fundamental question in Holography and Conformal Field Theory. After a pedagogical introduction covering the connections between these aspects, I will present a new consistency condition for the compatibility of a gravitational effective field theory in AdS with a dual holographic description. The condition amounts to the requirement that certain (properly defined) cubic interactions in the bulk must vanish. Remarkably, the constraint is satisfied for the well-known, scale-separated DGKT vacua in type IIA, thanks to a series of non-trivial cancellations. I will conclude with a possible bulk interpretation, as well as a future outlook.

Abstract:
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Asymptotic symmetries, sometimes also known as "large gauge transformations", provide important dynamical information on theories with a gauge freedom formulated on spacetimes having a "boundary at infinity". A review of asymptotic symmetries will be given following the Hamiltonian approach. General features (such as the form of the symmetry generators and the structure of the algebra) will be explained. The discussion will focus on gravity in the asymptotically flat context, where the relevant asymptotic symmetry algebra is the infinite-dimensional BMS algebra.

Abstract:
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A central challenge in string phenomenology is to understand the scalar potentials that arise from compactifications to lower-dimensional effective field theories. In recent years, the swampland program has called into question many earlier proposals for semi-realistic vacua in the string landscape. In this talk, I will review the relevant swampland conjectures and discuss the current status of proposed counterexamples. I will begin with the construction of four-dimensional N=1 Minkowski vacua with no massless scalar fields. I will then present recently discovered low-energy effective theories with negative cosmological constants - namely AdS vacua - arising in Type II and heterotic string compactifications on G2 spaces.

Abstract:
I will present nonthermal fixed points as paradigmatic far from equilibrium weak coupling phenomena characterised by a self-similar evolution in time. I will then discuss what strong coupling perspective based on the quasinormal modes insights into holographic thermalization and hydrodynamics can teach us about nonthermal fixed points. Based on 2307.07545, 2502.01622 and 2504.18754.

Abstract:
In the 1960s, the dominant approach to the strong interaction was the S-matrix bootstrap: the idea that the hadronic spectrum and scattering amplitudes could be determined from the general principles of causality and unitarity. This program culminated in the Veneziano amplitude which gave birth to string theory, but was abandoned as an approach to the strong force after the identification of Quantum Chromodynamics (QCD) as the microscopic theory of hadron physics. Yet QCD at low energies remains largely unsolved. Professor Rastelli will describe how modern bootstrap methods, powered new theoretical insights and computational techniques, allow us to revisit this classic program with unprecedented rigor.