Triangle Seminars
April 2026
Wed
1 Apr 2026
TBA
📍 London
Sayantani Bhattacharyya
(University of Edinburgh)
Abstract:
TBA
TBA
Posted by: Andrew Svesko
March 2026
Wed
25 Mar 2026
TBA
📍 London
Roberto Tateo
(INFN, Turin)
Abstract:
TBA
TBA
Posted by: Andrew Svesko
Thu
19 Mar 2026
TBA
📍 London
Kostas Skenderis
(Southampton)
Wed
18 Mar 2026
TBA
📍 London
Raju Venugopalan
(Stony Brook University)
Abstract:
TBA
TBA
Posted by: Andrew Svesko
Thu
5 Mar 2026
TBA
📍 London
Chris Hull
(Imperial College London)
Wed
4 Mar 2026
TBA
📍 London
Suman Kundu
(SISSA)
Abstract:
TBA
TBA
Posted by: Jesse van Muiden
Wed
4 Mar 2026
TBA
📍 London
Kelian Haring
(University of Amsterdam)
Abstract:
TBA
TBA
Posted by: Andrew Svesko
February 2026
Thu
26 Feb 2026
TBA
📍 London
Rafael Aoude
(Edinburgh)
Wed
25 Feb 2026
AI-Assisted Mathematical Discovery (Course)
📍 London
Nebius Academy
(Nebius)
Abstract:
This 14-week course explores how modern AI techniques can support mathematical research and problem-solving. It is not only an introduction to AI, but also a survey of its applications in math discovery, illustrated through research papers and coding tasks.
Course topics include:
- AI-assisted coding and reasoning. Running massive math experiments with the help of coding assistants. Using LLMs as research assistants.
- Training and using AI models. From linear models to neural networks: when AI models are useful and when they are not; data collection; model training.
- Transformers and LLMs. Mathematical data as sequences: from individual formulas to statements and proofs. The use of transformers and LLMs.
- Searching for examples and counterexamples. Speeding up search in huge search spaces. Algorithm optimization with AlphaEvolve and its open source analogs. Reinforcement Learning.
The course will be taught at the London Institute for Mathematical Sciences over 14 weeks, starting on February 25, with sessions held on Wednesdays from 10:00 am to 1:00 pm.
The programme is open to mathematicians and theoretical physicists, with proficiency in Python as a strong prerequisite.
For registration and more information on the course and Nebius Academy, visit: https://academy.nebius.com/ai-for-math?utm_source=lims&utm_medium=email&utm_campaign=limsnewsletter
This 14-week course explores how modern AI techniques can support mathematical research and problem-solving. It is not only an introduction to AI, but also a survey of its applications in math discovery, illustrated through research papers and coding tasks.
Course topics include:
- AI-assisted coding and reasoning. Running massive math experiments with the help of coding assistants. Using LLMs as research assistants.
- Training and using AI models. From linear models to neural networks: when AI models are useful and when they are not; data collection; model training.
- Transformers and LLMs. Mathematical data as sequences: from individual formulas to statements and proofs. The use of transformers and LLMs.
- Searching for examples and counterexamples. Speeding up search in huge search spaces. Algorithm optimization with AlphaEvolve and its open source analogs. Reinforcement Learning.
The course will be taught at the London Institute for Mathematical Sciences over 14 weeks, starting on February 25, with sessions held on Wednesdays from 10:00 am to 1:00 pm.
The programme is open to mathematicians and theoretical physicists, with proficiency in Python as a strong prerequisite.
For registration and more information on the course and Nebius Academy, visit: https://academy.nebius.com/ai-for-math?utm_source=lims&utm_medium=email&utm_campaign=limsnewsletter
Posted by: Evgeny Sobko
Wed
25 Feb 2026
TBA
📍 London
Matijn Francois
(Geneva University)
Abstract:
TBA
TBA
Posted by: Jesse van Muiden
Wed
25 Feb 2026
TBA
📍 London
Blaise Gouteraux
(Ecole polytechnique)
Abstract:
TBA
TBA
Posted by: Andrew Svesko
Thu
19 Feb 2026
TBA
📍 London
Jung-Wook Kim
(CERN)
Wed
18 Feb 2026
TBA
📍 London
Ilija Buric
(Trinity College Dublin)
Abstract:
TBA
TBA
Posted by: Jesse van Muiden
Wed
18 Feb 2026
TBA
📍 London
Andrei Parnachev
(Trinity College Dublin)
Abstract:
TBA
TBA
Posted by: Andrew Svesko
Wed
11 Feb 2026
TBA
📍 London
Lorenz Eberhardt
(University of Amsterdam)
Abstract:
TBA
TBA
Posted by: Jesse van Muiden
Wed
11 Feb 2026
TBA
📍 London
Shu-Heng Shao
(MIT, Cambridge)
Abstract:
TBA
TBA
Posted by: Jesse van Muiden
Thu
5 Feb 2026
TBA
📍 London
Enrico Pajer
(Cambridge)
Abstract:
TBA
TBA
Posted by: Nathan Moynihan
Wed
4 Feb 2026
TBA
📍 London
Silvia Penati
(Milan Bicocca University)
Abstract:
TBA
TBA
Posted by: Jesse van Muiden
Wed
4 Feb 2026
TBA
📍 London
Jahmall Bersini
(Albert Einstein Center for Fundamental Physics, Bern University)
Abstract:
TBA
TBA
Posted by: Andrew Svesko
Tue
3 Feb 2026
TBA
📍 London
Tin Sulejmanpasic
(Durham)
January 2026
Thu
29 Jan 2026
Novel properties of QFTs with long-range interactions
📍 London
Luke Lippstreu
(Edinburgh)
Abstract:
Infrared divergences obscure key analytic properties of scattering amplitudes, exposing gaps in our understanding of unitarity, causality, and crossing symmetry in theories with long-range forces. In this talk, I will use a simple model to illustrate novel analytic features of long-range theories, including modifications to the connectedness structure of amplitudes and to the general optical theorem. Since the LSZ reduction formula does not apply to theories with long-range forces, I will also present a modified version of LSZ reduction for this model, which accounts for long-range interactions and yields IR-finite amplitudes without ambiguous scales or ill-defined integrals.
Infrared divergences obscure key analytic properties of scattering amplitudes, exposing gaps in our understanding of unitarity, causality, and crossing symmetry in theories with long-range forces. In this talk, I will use a simple model to illustrate novel analytic features of long-range theories, including modifications to the connectedness structure of amplitudes and to the general optical theorem. Since the LSZ reduction formula does not apply to theories with long-range forces, I will also present a modified version of LSZ reduction for this model, which accounts for long-range interactions and yields IR-finite amplitudes without ambiguous scales or ill-defined integrals.
Posted by: Nathan Moynihan
Wed
28 Jan 2026
Relativistic Field Theories for Interacting Classical Higher-Spin Particles
📍 London
Radu Roiban
(Penn State University)
Abstract:
The construction of an effective field theory describing the long-distance interactions of Kerr black holes remains elusive.
As a step in its direction, we discuss relativistic effective field theories (EFT) designed to capture the long-distance gravitational interactions of massive spinning particles. While "no-go" theorems severely constrain the formulation of interacting higher-spin theories, we argue that these challenges can be navigated in the classical limit through the use of spin coherent states.
These states naturally incorporate gapless excitations which turn out to provide a description for processes in which the magnitude of the spin vector evolves dynamically.
By appropriately choosing the couplings of the theory these modes can either be decoupled, as we show by analyzing 3-point, Compton, and two-body amplitudes, or tuned to describe specific systems. We discuss the broader applicability of this framework, showing that it captures certain supersymmetric black holes as well as the dynamics of Newtonian bound states under external probes. Finally, we discuss possible strategies to identify the definition of Kerr black holes in this framework.
The construction of an effective field theory describing the long-distance interactions of Kerr black holes remains elusive.
As a step in its direction, we discuss relativistic effective field theories (EFT) designed to capture the long-distance gravitational interactions of massive spinning particles. While "no-go" theorems severely constrain the formulation of interacting higher-spin theories, we argue that these challenges can be navigated in the classical limit through the use of spin coherent states.
These states naturally incorporate gapless excitations which turn out to provide a description for processes in which the magnitude of the spin vector evolves dynamically.
By appropriately choosing the couplings of the theory these modes can either be decoupled, as we show by analyzing 3-point, Compton, and two-body amplitudes, or tuned to describe specific systems. We discuss the broader applicability of this framework, showing that it captures certain supersymmetric black holes as well as the dynamics of Newtonian bound states under external probes. Finally, we discuss possible strategies to identify the definition of Kerr black holes in this framework.
Posted by: Jesse van Muiden
Wed
28 Jan 2026
New Bounds on Null Energy in Quantum Field Theories
📍 London
Andrew Rolph
(Vrije U., Brussels)
Abstract:
Energy plays a ubiquitous role in physics. Many physical classical field theories obey pointwise energy conditions, and these have played an important role in, for example, singularity theorems. However, for local, relativistic quantum field theories (QFTs), the study of energy is both richer and more precarious. In this talk, I will derive new families of quantum null energy inequalities (QNEIs), i.e. bounds on integrated null energy, in QFTs in two and higher dimensions. These are universal, state-independent lower bounds on semi-local integrals of the energy-momentum flux in a null direction, and the first of this kind for interacting theories in higher dimensions. Our ingredients include the quantum null energy condition (QNEC), strong subadditivity of von Neumann entropies, defect operator expansions, and the vacuum modular Hamiltonians of null intervals and strips. These results are new, fundamental constraints on null energy in quantum field theories.
Energy plays a ubiquitous role in physics. Many physical classical field theories obey pointwise energy conditions, and these have played an important role in, for example, singularity theorems. However, for local, relativistic quantum field theories (QFTs), the study of energy is both richer and more precarious. In this talk, I will derive new families of quantum null energy inequalities (QNEIs), i.e. bounds on integrated null energy, in QFTs in two and higher dimensions. These are universal, state-independent lower bounds on semi-local integrals of the energy-momentum flux in a null direction, and the first of this kind for interacting theories in higher dimensions. Our ingredients include the quantum null energy condition (QNEC), strong subadditivity of von Neumann entropies, defect operator expansions, and the vacuum modular Hamiltonians of null intervals and strips. These results are new, fundamental constraints on null energy in quantum field theories.
Posted by: Andrew Svesko
Tue
27 Jan 2026
Deep Learning based discovery of Integrable Systems
📍 London
Evgeny Sobko
(LIMS)
Abstract:
Integrable systems are exactly solvable models that play a central role in QFT, string theory and statistical physics offering an ideal setting for understanding complex physical phenomena and developing novel analytical methods. However, the discovery of new integrable systems remains a major open challenge due to the nonlinearity of the Yang–Baxter equation (YBE) that defines them, and the vastness of its solution space. Here we present the first AI-based framework that enables the discovery of new quantum integrable systems in exact analytical form. Our
method combines an ensemble of neural networks, trained to identify high-precision numerical solutions to the YBE, with an algebraic extraction procedure based on the Reshetikhin integrability condition, which reconstructs the corresponding Hamiltonian families analytically. When applied to spin chains with three- and four-dimensional site spaces, we discover hundreds of previously unknown integrable Hamiltonians. Remarkably, these Hamiltonians organize into rational algebraic varieties, and we conjecture that this rationality holds universally — revealing a previously unexplored connection between quantum integrability and algebraic geometry. By unlocking inte-
grable systems far beyond the reach of traditional methods, this AI-driven approach substantially
expands the landscape of exactly solvable models and opens a scalable path to further discoveries.
Integrable systems are exactly solvable models that play a central role in QFT, string theory and statistical physics offering an ideal setting for understanding complex physical phenomena and developing novel analytical methods. However, the discovery of new integrable systems remains a major open challenge due to the nonlinearity of the Yang–Baxter equation (YBE) that defines them, and the vastness of its solution space. Here we present the first AI-based framework that enables the discovery of new quantum integrable systems in exact analytical form. Our
method combines an ensemble of neural networks, trained to identify high-precision numerical solutions to the YBE, with an algebraic extraction procedure based on the Reshetikhin integrability condition, which reconstructs the corresponding Hamiltonian families analytically. When applied to spin chains with three- and four-dimensional site spaces, we discover hundreds of previously unknown integrable Hamiltonians. Remarkably, these Hamiltonians organize into rational algebraic varieties, and we conjecture that this rationality holds universally — revealing a previously unexplored connection between quantum integrability and algebraic geometry. By unlocking inte-
grable systems far beyond the reach of traditional methods, this AI-driven approach substantially
expands the landscape of exactly solvable models and opens a scalable path to further discoveries.
Posted by: Sebastian Cespedes
Thu
22 Jan 2026
The Gravitational Compton Amplitude
📍 London
Mathias Driesse
(Humboldt)
Abstract:
The gravitational Compton amplitude describes gravitational waves scattering off a single black hole and is therefore a one-body observable ideal for analyzing quadratic-in-curvature of generic (Kerr) black holes from an effective field theory point of view. Based on upcoming work together with Y. Fabian Bautista, Gustav Jakobsen, and Kays Haddad, in this talk, I will discuss what makes it worth studying and calculating explicitly. I briefly review elements of black hole perturbation theory, which is the UV theory that describes such objects. I will then explain how worldline quantum field theory (WQFT) is an ideally suited tool to calculate the amplitude, focusing on similarities between this and the gravitation two-body problem which has recently been pushed to four loops. Finally, I will illustrate our matching procedure between these two theories, which allows us to calculate the Love numbers of black holes, with a particular focus on the N-matrix (Magnusian).
The gravitational Compton amplitude describes gravitational waves scattering off a single black hole and is therefore a one-body observable ideal for analyzing quadratic-in-curvature of generic (Kerr) black holes from an effective field theory point of view. Based on upcoming work together with Y. Fabian Bautista, Gustav Jakobsen, and Kays Haddad, in this talk, I will discuss what makes it worth studying and calculating explicitly. I briefly review elements of black hole perturbation theory, which is the UV theory that describes such objects. I will then explain how worldline quantum field theory (WQFT) is an ideally suited tool to calculate the amplitude, focusing on similarities between this and the gravitation two-body problem which has recently been pushed to four loops. Finally, I will illustrate our matching procedure between these two theories, which allows us to calculate the Love numbers of black holes, with a particular focus on the N-matrix (Magnusian).
Posted by: Nathan Moynihan
Wed
21 Jan 2026
An introduction to Open System Methods for Cosmology
📍 London
Thomas Colas
(University of Cambridge)
Abstract:
Effective field theories in particle physics are typically developed for clean, isolated systems, yet many physical phenomena, from condensed matter to gravitating systems, involve noisy and dissipative environments. The Schwinger-Keldysh formalism provides a powerful framework for describing such non-equilibrium dynamics and has led to important advances in areas including black hole physics, dissipative hydrodynamics, non-equilibrium holography, and primordial cosmology. I will begin with a pedagogical introduction to open-quantum-system techniques formulated within the Schwinger–Keldysh path integral. I will show how symmetries, locality, and unitarity constrain dissipation and noise, and illustrate the framework by deriving the imprints of dissipative dynamics on primordial non-Gaussianities. I will conclude by discussing the challenge of formulating general relativity in the presence of an unspecified medium.
Effective field theories in particle physics are typically developed for clean, isolated systems, yet many physical phenomena, from condensed matter to gravitating systems, involve noisy and dissipative environments. The Schwinger-Keldysh formalism provides a powerful framework for describing such non-equilibrium dynamics and has led to important advances in areas including black hole physics, dissipative hydrodynamics, non-equilibrium holography, and primordial cosmology. I will begin with a pedagogical introduction to open-quantum-system techniques formulated within the Schwinger–Keldysh path integral. I will show how symmetries, locality, and unitarity constrain dissipation and noise, and illustrate the framework by deriving the imprints of dissipative dynamics on primordial non-Gaussianities. I will conclude by discussing the challenge of formulating general relativity in the presence of an unspecified medium.
Posted by: Riccardo Gonzo
Wed
21 Jan 2026
Scattering on the Coulomb Branch of \(\mathcal{N}=4\) SYM
📍 London
Kelian Haring
(University of Amsterdam)
Abstract:
I will discuss scattering on the Coulomb branch of planar N=4 SYM at finite ’t Hooft coupling. This describes a family of classical open-string S-matrices that smoothly interpolates between perturbative parton scattering at weak coupling and flat-space string scattering at strong coupling. I will focus on the four-point amplitude and discuss its remarkably rich structure: nonlinear Regge trajectories, dual conformal invariance, an intricate spectrum of bound states with an accumulation point, and a two-particle cut. Using dispersion relations and S-matrix bootstrap techniques, these properties can be incorporated to constrain the amplitude at finite ’t Hooft coupling, and I will discuss bounds on Wilson coefficients, couplings to bound states, and the overall shape of the amplitude.
This talk is based on https://arxiv.org/abs/2510.19909.
I will discuss scattering on the Coulomb branch of planar N=4 SYM at finite ’t Hooft coupling. This describes a family of classical open-string S-matrices that smoothly interpolates between perturbative parton scattering at weak coupling and flat-space string scattering at strong coupling. I will focus on the four-point amplitude and discuss its remarkably rich structure: nonlinear Regge trajectories, dual conformal invariance, an intricate spectrum of bound states with an accumulation point, and a two-particle cut. Using dispersion relations and S-matrix bootstrap techniques, these properties can be incorporated to constrain the amplitude at finite ’t Hooft coupling, and I will discuss bounds on Wilson coefficients, couplings to bound states, and the overall shape of the amplitude.
This talk is based on https://arxiv.org/abs/2510.19909.
Posted by: Jesse van Muiden
Wed
21 Jan 2026
Recent Progress on Axions from Calabi-Yau Compactifications: Observational Data Meets String Theory
📍 London
David Marsh
(King's College London)
Abstract:
The past few years have seen major advances in understanding the properties of axions in string theory. This progress is thanks to new computational tools that allow for fast and automated calculations with Calabi-Yau manifolds. I will describe the predictions string theory makes for axion masses, decay constants, and axion-photon couplings, and how these depend precisely on the topology of the Calabi-Yau. I will describe explicit constructions of millions of axiverse models on Calabi-Yaus with Hodge numbers up to 491, across the whole Kreuzer-Skarke database (and some results beyond this). Phenomenology computed includes: black hole superradiance, dark matter relic density, fuzzy dark matter, decaying heavy relics and the intergalactic medium, and the QCD axion mass. I will describe the correlation between QCD axion mass and topology, and how this makes it possible for axion "haloscope" experiments to experimentally infer Hodge numbers, divisor topologies, and moduli space loci. I demonstrate the statistical state of the art by computing a full forward model incorporating likelihoods from the cosmic microwave background and Lyman-alpha forest and find the maximum Bayesian posterior probability region on the moduli space of a given CY favoured by a resolution of the tension in these data by an ultralight axion composing 1% of the dark matter.
The past few years have seen major advances in understanding the properties of axions in string theory. This progress is thanks to new computational tools that allow for fast and automated calculations with Calabi-Yau manifolds. I will describe the predictions string theory makes for axion masses, decay constants, and axion-photon couplings, and how these depend precisely on the topology of the Calabi-Yau. I will describe explicit constructions of millions of axiverse models on Calabi-Yaus with Hodge numbers up to 491, across the whole Kreuzer-Skarke database (and some results beyond this). Phenomenology computed includes: black hole superradiance, dark matter relic density, fuzzy dark matter, decaying heavy relics and the intergalactic medium, and the QCD axion mass. I will describe the correlation between QCD axion mass and topology, and how this makes it possible for axion "haloscope" experiments to experimentally infer Hodge numbers, divisor topologies, and moduli space loci. I demonstrate the statistical state of the art by computing a full forward model incorporating likelihoods from the cosmic microwave background and Lyman-alpha forest and find the maximum Bayesian posterior probability region on the moduli space of a given CY favoured by a resolution of the tension in these data by an ultralight axion composing 1% of the dark matter.
Posted by: Andrew Svesko
Tue
20 Jan 2026
From black holes to solvable irrelevant deformations and back
📍 London
Monica Guica
(IPhT)
Abstract:
String theory has been remarkably successful in explaining the microscopic origin of the entropy of certain black holes, primarily supersymmetric ones. However, finding the microscopic description of more realistic black holes remains a challenging open problem. In this talk, I will review evidence suggesting that the microscopic description of near- and non-extremal black holes is governed by special irrelevant deformations of two-dimensional conformal field theories. I will then discuss the properties of a particular class of solvable irrelevant deformations of two-dimensional quantum field theories, known as TT– and JTˉJ\bar-deformed CFTs. Finally, I will discuss the lessons that recent progress in understanding these deformations offers for the microscopic description of general black holes.
String theory has been remarkably successful in explaining the microscopic origin of the entropy of certain black holes, primarily supersymmetric ones. However, finding the microscopic description of more realistic black holes remains a challenging open problem. In this talk, I will review evidence suggesting that the microscopic description of near- and non-extremal black holes is governed by special irrelevant deformations of two-dimensional conformal field theories. I will then discuss the properties of a particular class of solvable irrelevant deformations of two-dimensional quantum field theories, known as TT– and JTˉJ\bar-deformed CFTs. Finally, I will discuss the lessons that recent progress in understanding these deformations offers for the microscopic description of general black holes.
Posted by: Sebastian Cespedes
Thu
15 Jan 2026
Automorphic L-functions, primon gases and quantum cosmology
📍 London
Sean A. Hartnoll
(Cambridge U., DAMTP)
Abstract:
I will review how the equations of general relativity near a spacetime singularity map onto an arithmetic hyperbolic billiard dynamics. The semiclassical quantum states for this dynamics are Maaβ cusp forms on fundamental domains of modular groups. For example, gravity in four spacetime dimensions leads to PSL(2,Z) while five dimensional gravity leads to PSL(2,Z[w]), with Z[w] the Eisenstein integers. The automorphic forms can be expressed, in a dilatation (Mellin transformed) basis as L-functions. The Euler product representation of these L-functions indicates that these quantum states admit a dual interpretation as a "primon gas" partition function. I will describe some physically motivated mathematical questions that arise from these observations.
I will review how the equations of general relativity near a spacetime singularity map onto an arithmetic hyperbolic billiard dynamics. The semiclassical quantum states for this dynamics are Maaβ cusp forms on fundamental domains of modular groups. For example, gravity in four spacetime dimensions leads to PSL(2,Z) while five dimensional gravity leads to PSL(2,Z[w]), with Z[w] the Eisenstein integers. The automorphic forms can be expressed, in a dilatation (Mellin transformed) basis as L-functions. The Euler product representation of these L-functions indicates that these quantum states admit a dual interpretation as a "primon gas" partition function. I will describe some physically motivated mathematical questions that arise from these observations.
Posted by: Morteza S. Hosseini
Wed
14 Jan 2026
Solving the AdS3/CFT2 duality
📍 London
Alessandro Sfondrini
(Birmingham University)
Abstract:
The correspondence between strings on AdS3 and dual CFT2s is one of the cornerstones of holography since its very inception. In the last few years there has been a remarkable revival of activity and progress in understanding quantitatively (i.e., solving) this duality. In this blackboard talk, I will present a pedagogical review of this progress and point out the exciting challenges which lie ahead.
Reference literature: A recent review of the subject can be found in arXiv:2408.08414
The correspondence between strings on AdS3 and dual CFT2s is one of the cornerstones of holography since its very inception. In the last few years there has been a remarkable revival of activity and progress in understanding quantitatively (i.e., solving) this duality. In this blackboard talk, I will present a pedagogical review of this progress and point out the exciting challenges which lie ahead.
Reference literature: A recent review of the subject can be found in arXiv:2408.08414
Posted by: Jesse van Muiden
Tue
13 Jan 2026
TBA
📍 London
Aron Wall
(University of Cambridge)
Abstract:
TBA
TBA
Posted by: Sebastian Cespedes
Wed
7 Jan 2026
TBA
📍 London
Charles Thull
(City University of London)
Abstract:
TBA
TBA
Posted by: Jesse van Muiden