Triangle Seminars

Abstract:
We will discuss how to bootstrap string theory in AdS, using N=4 SYM as a concrete example. The first lecture will review the basic ingredients of AdS/CFT: the definitions of AdS and CFT, the correspondence between Kaluza–Klein modes and single-trace operators, and the relation between string scattering in AdS and correlation functions of Kaluza–Klein modes in the CFT. The second lecture will focus on the stress-tensor multiplet four-point function, including its conformal block expansion, the constraints imposed by superconformal Ward identities, and its formulation in Mellin space. The third lecture will introduce the flat-space limit, explain how it acts on the conformal block expansion, and discuss the spectrum of single-trace operators that survives at strong coupling. In the final lecture, we will go beyond the flat-space limit and study the first AdS correction. We will introduce a worldsheet ansatz for this correction and show how matching it to the conformal block expansion fixes the correction completely.

Abstract:
Registration Please fill in this form https://tally.so/r/rj7axl to confirm your attendance at Geordie’s talk, so we have a clearer idea of numbers. It's free but due to popularity please sign up.



Almost every week brings another AI breakthrough in mathematics—and fresh questions about the future of the field, its practitioners and humanity itself. In this AI for Mathematical Sciences seminar, Prof. Geordie Williamson sets aside predictions about what AI might achieve and turns instead to how humans do mathematics.

Williamson examines the choices and intuitions that shape mathematical thought. He considers where definitions come from, what purpose they serve and how they help mathematicians explore unfamiliar ideas. He also explores the role of prediction in research, from recognising patterns to anticipating what might be true.

Finally, he considers whether geometry plays a fundamental part in mathematics, even in areas far removed from shapes and space. Rather than forecasting what machines may soon prove, the talk takes AI’s rise as an occasion to reflect on the human mathematical process: how mathematicians think, what guides their work and what they value in it.

Abstract:
TBA

Abstract:
I will review a series of impressive numerical calculations from the 90s that revealed universal scaling behaviour in gravitational collapse. I will then focus on spherically symmetric perfect fluid collapse and explain how treating the number of spacetime dimensions, D, as an expansion parameter gives us analytic control of its continuously self-similar critical solution. In a 1/D expansion, we construct this solution and compute its critical exponent. At leading order, the length-scaling exponent is 1/2 and does not depend on the fluid’s equation of state parameter, a simplification reminiscent of mean-field behaviour. This rich system provides many potential routes for exploring universality in classical gravity. Based on a series of forthcoming papers with Guilherme L. Pimentel.

Abstract:
BPS decoupling limits of string and M-theory have led to profound insights into gravity and non-perturbative quantum theory, most notably with the AdS/CFT correspondence. A large class of such limits are related by U-duality to discrete lightcone quantization limits (DLCQs). However, there are natural BPS decoupling limits within the AdS/CFT correspondence that cannot be seen as DLCQ limits. Therefore, we introduce a new kind of BPS decoupling limit in which the relevant BPS states carry momentum along circle fibers geometrically twisted over a base space, unlike for a DLCQ limit. In the AdS/CFT correspondence these limits are associated with BPS states of the global symmetry algebra  PSU(2,2|4). In general, string fluctuations in a twisted BPS decoupling limit are described by non-relativistic sigma-models on emergent non-Lorentzian target spaces with a natural symplectic structure. This  further supports the broader connection between BPS limits and non-Lorentzian geometry. We introduce analogous limits of D-branes as well, probing the same symplectic structure as the string. For AdS/CFT, these results point to corners with tractable and explicit quantum-mechanical descriptions of non-perturbative regimes.

Abstract:
Black holes contain spacetime singularities, at which tidal forces become infinite and time ends. The approach to these singularities is believed to be chaotic and yet governed, on average, by a deep number-theoretic symmetry known as modularity. The outside of a black hole, in contrast, is highly regular. Any feature is rapidly hoovered up by the black hole itself and an external observer will witness only a "ringdown", the wobbles of the event horizon as it returns to equilibrium. A low-frequency so-called "quasinormal mode" of this ringdown was detected in 2015 by gravitational wave experiments. It has been known for two decades that very high frequency quasinormal modes are sensitive to the behaviour of spacetime close to the singularity, via a mathematical process known as analytic continuation. I will explain recent work that has shown how the chaotic near-singularity dynamics can be heard by listening carefully to the quasinormal modes.


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Please register for the event:
https://lims.ac.uk/event/can-one-hear-the-shape-of-a-black-hole-singularity/

Colloquium at 4:30 PM, 21 Oct 2026 at LIMS, 2F of Royal Institution, 21 Albemarle St, W1S4BS, London

Abstract:
TBD.