Triangle Seminars

Abstract:
Holography maps a thermal ensemble of a QFT to a black hole. Infall inside the black hole enables 1pt functions for local operators. In the spin-chain description of 1pt functions, the black hole maps to a boundary state with quite unusual features that I will describe. The state breaks integrability, has a logarithmic entanglement entropy and thermalizes at infinite temperature. This can be confronted with 1pt function arising from D-branes, which preserve integrability and in some cases can be computed exactly by Bethe Ansatz.

Abstract:
Thermal conformal field theories (CFTs) describe quantum systems at finite temperature, with applications ranging from laboratory systems to the holographic description of black holes. Although the thermal background breaks global conformal symmetry, key local data of the zero-temperature theory—such as the spectrum and operator product expansion—remain intact. Thermal correlators are further constrained by the Kubo–Martin–Schwinger (KMS) condition, which enforces periodicity along the thermal circle and plays a role analogous to crossing symmetry in zero-temperature systems. Placing the theory at finite volume enriches this structure and, in holographic settings, allows for the emergence of distinct phases.
In this talk, I will present analytic and numerical bootstrap approaches to solving the KMS condition for thermal two-point functions. These methods reconstruct correlators from minimal input and apply across weakly and strongly coupled regimes. I will illustrate them in free theories, O(N) models, and holographic CFTs, and conclude with a brief outlook on ongoing developments.

Abstract:
Any UV complete theory of gravity typically in its low energy classical limit will generate higher derivative corrections to Einstein's General Theory of Relativity (GTR). GTR admits the black hole solution which satisfies the laws of thermodynamics. Black hole solutions continue to exist classically in presence of perturbative higher derivative corrections. Also, we expect the black hole to satisfy the same thermodynamic laws at least order by order in an expansion in higher derivative couplings. However, we still do not have any completely satisfactory proof or counter example for this expectation. In this talk we shall discuss how we have approached this problem in a classical setting and the current status of our understanding. 

Abstract:
In this second talk in the AI for Mathematical Sciences (AIMS) seminar series Dr Adam Zsolt Wagner explores the frontiers of automated mathematical discovery. With an emphasis on his work at Google DeepMind, he discusses tools such AlphaEvolve that aim to bridge the gap between human intuition and the vast space of potential mathematical constructions. By treating mathematical problems as search tasks within “language space” these tools can generate counterexamples, find novel configurations and significantly reduce the manual effort required to explore ideas and test complex hypotheses.

Dr Wagner demonstrates how these AI-driven approaches are being applied to problems in combinatorics and beyond. He discusses the mechanics of FunSearch and AlphaEvolve, shares insights from collaborative work with Javier Gomez-Serrano and Terence Tao and provides a framework for mathematicians and theoretical physicists to determine which AI search strategies are best suited for their own research.

To subscribe for the AIMS series please fill out the form https://applications.lims.ac.uk/subscribe-to-aims