Black holes hide spacetime singularities, where tidal forces become infinite and time comes to an end. The approach to a singularity is thought to be chaotic, yet its average behaviour may follow a deep number-theoretic symmetry known as modularity.

Outside a black hole, the picture is very different. Disturbances rapidly die away, leaving a characteristic ‘ringdown’ as the black hole settles back into equilibrium. Gravitational-wave observations in 2015 detected a low-frequency quasinormal mode associated with this ringing. For two decades, physicists have known that much higher-frequency modes encode information about spacetime near the singularity, accessible through a mathematical technique called analytic continuation.

In this colloquium, Prof. Sean Hartnoll explains recent work connecting these two seemingly opposed regimes. He shows how the chaotic dynamics near a black hole’s singularity leave a trace in its quasinormal modes—and how listening to that ringing can reveal the mathematics of the black hole’s interior.

## Event information

This event takes place at 4:30pm on Wednesday 21 October in the Faraday seminar room of the London Institute for Mathematical Sciences, on the second floor of the Royal Institution. LIMS colloquia are sponsored by Cognia.

Sean Hartnoll shows how the ringing of black holes reveals chaotic dynamics near their singularities and hints at hidden mathematical order.

A singularity's echo

Can one hear the shape of a black hole singularity?

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.

## Event information
This event, part of our AI for Mathematical Sciences series, takes place at 4 pm on Monday 19 October at the London Institute for Mathematical Sciences, on the second floor of the Royal Institution. AIMS is sponsored by Nebius. This series is organised by LIMS fellows [Prof. Yang-Hui He](https://lims.ac.uk/yang-hui-he/) and [Dr Evgeny Sobko](https://lims.ac.uk/evgeny-sobko/). To register for the series please fill out the [online form](https://applications.lims.ac.uk/subscribe-to-aims).

Geordie Williamson explores what AI’s rise reveals about how humans do mathematics, from definitions and prediction to the role of geometry.

What maths means to us

AI and the process of human mathematics

How can string theory in anti-de Sitter (AdS) space be reconstructed? Using N=4 supersymmetric Yang–Mills theory (SYM) as an example, Dr Shai Chester explores this question through the AdS/CFT correspondence.

The first lecture introduces AdS and conformal field theories (CFTs), the link between Kaluza–Klein modes and single-trace operators, and how string scattering in AdS relates to CFT correlation functions. The second examines the four-point function of the stress-tensor multiplet, its conformal block expansion, the constraints of superconformal Ward identities, and its description in Mellin space.

The third lecture takes the flat-space limit, tracing its effect on the conformal block expansion and identifying the single-trace spectrum that survives at strong coupling. The final lecture goes beyond this limit to the first AdS correction. Dr Chester introduces a worldsheet ansatz and shows how matching it to the conformal block expansion determines the correction completely.

## Event information

This is a four-part lecture series from LonTI Lectures are on Mondays at 10:30 am in the seminar room at the London Institute, on the second floor of the Royal Institution, followed by drinks and snacks onsite. To register and attend, please visit [LonTI website](https://lonti.weebly.com/).

Shai Chester explores how to bootstrap string theory in AdS using AdS/CFT, from conformal blocks to the first correction beyond flat space.

Bootstrapping strings

Bootstrapping string theory

Gergely Bérczi is an associate professor of mathematics at Aarhus University and head of the Aarhus DFF Algebraic Geometry Group.

Confirmed speaker

Prof. Williamson is a rare mathematician, working at the frontiers of both pure mathematics and AI-assisted discovery. In this event, he joins the London Institute's chief science writer Ananyo Bhattacharya to discuss the path from a country childhood in New South Wales to the deepest questions in representation theory, and what mathematics means to him.

That question is newly urgent. In barely a year, machines have taken olympiad gold, felled a string of Erdős problems and produced a contested, Lean-checked proof that Navier–Stokes solutions can blow up. More such proofs are rumoured to be weeks away. Prof. Williamson, who worked with DeepMind on knot theory, asks how much of this is mathematics and how much pattern-matching at scale.

Much follows from the answer: whether proof, taste and understanding survive automation, how young mathematicians should train and how institutes can keep human insight at their heart.

There will be time for audience questions followed by drinks.

## Event information

The event is on Monday 19 October at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. Entry is by invitation only. There are drinks in the Old Post room from 5:30 pm, and the interview starts at 6 pm in our Faraday seminar room, followed by a Q&A with the audience from 6:50 pm. Afterwards there are drinks with the speaker into the evening in the Faraday and Old Post rooms.

Geordie Williamson discusses the nature of mathematical discovery, the impact of AI and the future of mathematics as a human profession.

Meet Prof. Williamson

Meet Geordie Williamson

Whether the six-dimensional sphere carries a complex structure is a longstanding puzzle. Dr Nikon Kurnosov examines a recent AI-assisted construction by Claude, guided by Levent Alpöge. Drawing on Phil Engel’s geometric account, he sets out the problem and explains the approach to the proof. The talk begins at a level accessible to those with undergraduate mathematics before moving into more advanced details of the proof.

[Dr Nikon Kurnosov](https://lims.ac.uk/nikon-kurnosov/) is a Khodorkovsky Research Fellow at the London Institute. He holds degrees in mathematics, chemistry and materials science, and has two PhDs. His work focuses on complex geometry, hyperkähler geometry, Calabi-Yau manifolds, algebraic geometry and automorphisms.

Nikon Kurnosov explains Claude’s proposed solution to the six-dimensional sphere puzzle, using Phil Engel’s geometric account of the proof.

Making sense of S⁶

Could the apparently continuous world of mathematics and physics be an approximation to a fundamentally finite universe? Over two lectures, Prof. Boris Zilber explores this possibility through model theory, the study of theories and their models.

At the heart of his talks is global approximation. Rather than treating a finite model as a local discretisation of a continuous theory, Prof. Zilber asks whether one sufficiently large finite structure can approximate an entire continuous structure, not merely isolated pieces of it. He shows how this approach leads to compact complex structures and considers what it might mean for our understanding of spacetime and fundamental physics.

Examples range from finite cyclic models of spacetime and Lorentz symmetry to quantum mechanics and structures arising in string theory. Zilber also examines the distinction between a global mathematical structure and the local coordinates and measurements an observer reconstructs from it.

## Event information

These two lectures will both be held in Faraday’s Study at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. The first, on Wednesday 30 September, begins at 3 o’ clock.  The second is at 2 o’ clock on the next day, Thursday 1 October.

Boris Zilber explores whether a finite structure can approximate the continuous world, with implications for spacetime and quantum theory.

Beyond the continuum

Model theory and the hypothesis of a finite universe

Chevalley groups are families of matrix groups built from rings. But if only the abstract group is known, can the original ring still be recovered? Prof. Elena Bunina explains how automorphisms—transformations that preserve a group’s structure—reveal this hidden ring, and how model theory makes the reconstruction precise. Twisted Chevalley groups may also retain the additional automorphism used in their construction.

[Elena Bunina](https://math.biu.ac.il/en/node/3476) is a professor of mathematics at Bar-Ilan University and Head of Nebius Academy, the education and research arm of AI cloud company Nebius. She studies algebra and model theory, including Chevalley groups and their automorphisms. She also serves on the Nebius board.

Elena Bunina shows how matrix groups retain a hidden record of the algebraic data used to build them, even when their origins are unknown.

Reconstructing rings

Can a matrix group remember how it was built?

Complex systems map many microscopic descriptions onto few macroscopic outcomes. Surprisingly, these input-output maps favor simple outputs. We prove that, in an exactly solvable deep-layered machine, depth drives the output distribution toward exponential decay in complexity. Thus hierarchical composition alone generates an intrinsic Occam's razor, giving an analytical explanation for simplicity bias in learning.
[Dr Thomas Fink](https://lims.ac.uk/thomas-fink/) is the founding Director of the London Institute and Charge de Recherche in the French CNRS. He studied physics at Caltech, Cambridge and École Normale Supérieure. His work includes statistical physics, combinatorics and the mathematics of evolvable systems.

Thomas Fink shows how a hierarchical composition naturally favours simple outputs, revealing an intrinsic Occam’s razor in layered systems.

Simplicity runs deep

Deep-layered machines have a built-in Occam's razor

Mutation and recombination are fundamental mechanisms of evolution, generating variation in DNA as organisms replicate. Using geometry and combinatorics, Roman Belavkin compares how each moves DNA sequences towards a fitter target. Mutation becomes less likely to help as the target nears, while recombination remains balanced, suggesting it can complement mutation and sustain evolutionary progress close to an optimum.
[Dr Roman Belavkin](https://www.mdx.ac.uk/about-us/our-people/staff-directory/dr-roman-belavkin/) is an associate professor in informatics at Middlesex University. He studies AI and information dynamics, optimal learning, evolutionary systems and the geometry of information. Beyond academia, he is an electronic musician known as Solar X and a master of kung fu.

Roman Belavkin explains why mutation slows near an evolutionary optimum, while recombination can keep adaptation moving by reshuffling DNA.

How evolution searches

Mutation and recombination: how they differ—lessons from mathematical analysis

Quantum field theory describes nature at its deepest, yet many of its core phenomena remain hard to compute. Jiunn-Wei Chen presents two recent quantum-computer calculations: parton distributions in the Schwinger model and thermalisation in SU(2) lattice gauge fields. The talk explains how quantum simulation probes real-time dynamics, relativistic bound states and how thermal behaviour emerges from unitary evolution.
-----
[Jiunn-Wei Chen](https://www.phys.ntu.edu.tw/enphysics/jwc.html) is a Distinguished Professor of Physics at National Taiwan University, where he directs the Center for Theoretical Physics. A nuclear theorist, he works on effective field theory, weak interactions, lattice QCD, quantum phases and the cosmological constant problem. 

Jiunn-Wei Chen shows how quantum computers can turn field theory into a laboratory for particles and gauge fields coming to equilibrium.

Qubits for QFT

Watching quantum fields evolve: partons and thermalisation on quantum computers

Algebraic geometry continues to develop through its interactions with representation theory, topology, singularity theory and mathematical physics. This workshop brings together researchers working across these neighbouring fields to explore the geometric structures, methods and ideas that connect them, as well as the questions they open.

The programme ranges from the birational geometry of singular varieties and the topology of hyperplane arrangement complements to geometric representation theory, symplectic duality and finite W-algebras. Rather than focusing on a single theme, the workshop highlights the breadth of modern geometry and the value of bringing diverse perspectives into dialogue.

By creating opportunities for discussion across different areas of geometry, the workshop aims to deepen participants’ understanding of contemporary research, encourages interdisciplinary exchange and opens new routes to future collaboration through lasting shared problem-solving.

## Event information
This workshop takes place on Tuesday 14 July at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution in Mayfair. All researchers with an interest in these topics are invited to attend. No registration is required. 

## Programme
- *10:00am* Arrival
- *10:30am* Dr Matt Booth, “Classifying singular threefold flops”
- *11:45am* Dr Matt Westway, “One-dimensional representations of finite W-algebras”
- *12:45pm* Lunch break
- *1:30pm* Dr Vasya Krylov, “Higgs, Coulomb branches and Symplectic duality”
- *2:30pm* Prof. Dmitri Panov, “Flat connections on complements to hyperplane arrangements”
- *3:30pm* Discussion


The London Institute hosts a workshop on algebraic geometry focusing on deformation theory, representation theory and birational geometry.

Aspects of geometry

There is a curious difference between muscle and mind. Muscles work when they work and rest when they rest. The mind, by contrast, often works while it rests and rests while it works but can it nevertheless be guided to perform better?

In this talk, Dr Mithu Storoni, author of *Hyperefficient*, examines the science of mental performance and creativity. She argues that assumptions developed for managing physical labour were mistakenly applied to knowledge work, creating a false equivalence between mental and physical productivity. The result is often workplace practices that optimise process rather than outcomes.

Drawing on neuroscience, physiology and psychology, Dr Storoni explores how mental efficiency emerges from the interaction of brain, body and environment. She discusses why effort alone is often a poor guide to performance, how creativity and insight arise, and presents practical techniques for improving productivity and performance in mentally-challenging work.

## Event information
The event is on Tuesday 30 June at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. Entry is by invitation only. Arrival is from 5:30pm in the Old Post Room. The talk starts at 6 pm in our Faraday seminar room,  and is followed by a Q&A with the audience. Afterwards there are drinks with the speaker into the evening in the Faraday and Old Post rooms.

Mithu Storoni explores the science of mental performance, revealing how to cultivate productivity, creativity, focus and sustained insight.

Being hyperefficient

Speaker

The neuroscience of creativity and focus

Music and mathematics are both arts that deal in patterns. In this event, a scientific exploration of music is paired with a piano recital, combining two complementary ways of appreciating sound, structure and beauty.

Inspired by a conversation at a recent London Institute event, Dr Thore Graepel explores if the concept of the octave can be brought into the visual domain. In this talk, he presents a new approach to visualising music, demonstrating a tool that allows audiences to hear and see music in real time and in kaleidoscopic glory. 

His talk is followed by a recital from celebrated concert pianist Sasha Grynyuk featuring works by Chopin, Liszt and Ravel—composers spanning the evolution of the piano across a century of musical innovation. Chopin helped define the Romantic piano idiom, Liszt vastly expanded its technical and expressive possibilities, and Ravel created his works at a moment when the modern French school was reshaping pianistic colour and texture.

## Event information
The event takes place on Wednesday 1 July at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. Attendance is by invitation only. Arrival is from 5:30pm in the Old Post Room. Dr Graepel’s talk begins at 6 pm. The concert, which will be held in Faraday’s Study, begins at 6.20pm and is followed by drinks into the evening.


## Programme
- *5:30pm* Arrival and drinks, Old Post Room
- *6:00pm* Dr Thore Graepel, “See Music!”
- *6:20pm* Sasha Grynyuk plays Maurice Ravel, Valses nobles et sentimentales; Frédéric Chopin, Scherzo No. 1 and Franz Liszt, Variationen über das Motiv von Bach: Weinen, Klagen, Sorgen, Zagen, S.180
- *7:00pm* Drinks, Old Post room

Music is seen as well as heard, with our governor Thore Graepel’s visualisation of sound, and a recital by acclaimed pianist Sasha Grynyuk.

The shape of music

Performers and speakers

String theory is a remarkably rich and complex framework, generating some of the largest data sets in contemporary theoretical physics. This abundance makes it a fertile ground for new ideas, but also presents a major challenge when attempting to connect its structures to known particle physics and observable physical phenomena.

In his talk for the AI for Mathematical Sciences (AIMS) seminar series, Prof. Andre Lukas gives an informal introduction to string theory and outlines how modern computational methods can help navigate its complexity. The discussion highlights how machine learning techniques can be used to analyse and explore the vast “landscape” of string theory models and related high-dimensional data.

The approaches he discusses include supervised learning to uncover patterns in mathematical data, heuristic searches using reinforcement learning and genetic algorithms, as well as self-supervised methods for solving differential equations arising in the theory.

## Event information

This event, part of our AI for Mathematical Sciences series, takes place at 2 pm on Thursday 14 May at the London Institute for Mathematical Sciences, on the second floor of the Royal Institution. AIMS is sponsored by Nebius. This series is organised by LIMS fellows [Prof. Yang-Hui He](https://lims.ac.uk/yang-hui-he/) and [Dr Evgeny Sobko](https://lims.ac.uk/evgeny-sobko/). To register for the series please fill out the [online form](https://applications.lims.ac.uk/subscribe-to-aims).

Andre Lukas shows how machine learning tackles string theory’s vast data, uncovering patterns, exploring its landscape and solving equations.

AI meets string theory

Machine learning, string theory and particle physics

Observations of the universe across the largest and smallest accessible scales reveal a striking simplicity, in tension with prevailing theories that predict a slew of new particles, forces, extra dimensions and even a chaotic multiverse. 

In this lecture, Prof. Neil Turok argues that these observations should prompt a rethinking of basic assumptions, and outlines a simpler, unified paradigm grounded in the known laws of physics and CPT symmetry.

Prof. Turok shows how this framework accounts for the large-scale structure of the universe and primordial density perturbations without inflation, identifies dark matter with a right-handed neutrino without additional beyond-standard-model particles, and explains the existence of three generations of elementary particles without recourse to string theory.

The proposal offers new insights into quantum gravity, the Big Bang and the arrow of time as well as a possible resolution of the long-standing gauge-gravity hierarchy puzzle.

### Event information
This event takes place at 4:30pm on Wednesday 13 May in the Faraday seminar room of the London Institute for Mathematical Sciences, on the second floor of the Royal Institution. LIMS colloquia are sponsored by Cognia.

Neil Turok presents a minimal paradigm for cosmology that explains the universe’s large-scale structure, dark matter and the Standard Model.

A simpler cosmology

London Institute Fellows Dr Mikhail Burtsev and Prof. Yang-Hui He chart the technical frontiers of AI and its implications for science and the economy in two complementary talks for invited guests.

Dr Burtsev discusses his work on overcoming the context-length limits of modern transformer models. He introduces architectures that incorporate explicit recurrent memory, enabling models to retain and retrieve information across long sequences. These approaches move transformers beyond fixed-window processing to streaming systems with trainable state, allowing efficient modelling of large-scale text, logs and time series.

In his talk, Prof. He reflects on the wider trajectory of machine intelligence and its growing role in the mathematical sciences. He considers how AI systems are reshaping discovery and what their rise reveals about computation, knowledge and the nature of intelligence.

There will be time for audience questions and discussion over drinks with the speakers.

## Event information
The event takes place on Monday 18 May at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. Entry is by invitation only.

## Programme
- *5:00pm* Arrival and drinks, Old Post Room
- *5:30pm* Prof. Yang-Hui He, Introduction, Faraday seminar room
- *5:35pm* Dr Mikhail Burtsev, “Breaking the context barrier.”
- *6:05pm* Prof. Yang-Hui He, “The rise of the machines.”
- *6:30pm* Drinks, Old Post room


Mikhail Burtsev and Yang-Hui He explore advances in AI, from long-context transformers to the impact of machine intelligence on science.

Frontiers of AI

Speakers

Prof. Neil Turok is Higgs Chair of Theoretical Physics at the University of Edinburgh and Emeritus Director of the Perimeter Institute for Theoretical Physics.

Prof. Turok stands at the forefront of debates about the origin of the universe and the future of fundamental physics. In this event, he joins the London Institute’s chief science writer Ananyo Bhattacharya to discuss his career and where the field now stands—from unresolved puzzles in cosmology and quantum gravity to the search for new guiding principles. Turning to the opportunities and risks posed by AI, he then focuses on what the technology means for the future practice of theoretical physics.

Drawing on his experience of leading the Perimeter Institute, Prof. Turok also addresses the challenges of building and sustaining institutes for fundamental research: how to set priorities, nurture talent and create environments in which new ideas can flourish.

There will be time for audience questions followed by drinks.

### Event information 

The event is on Wednesday 13 May at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. Entry is by invitation only. The interview starts at 6 pm in our Faraday seminar room, followed by a Q&A with the audience from 6:50 pm. Afterwards there are drinks with the speaker into the evening in the Faraday and Old Post rooms.

Neil Turok discusses the future of theoretical physics, the impact of AI and how to build and lead institutes for fundamental research.

Meet Neil Turok

In this third talk in the AI for Mathematical Sciences (AIMS) seminar series, Prof. Javier Gómez-Serrano explores how machine learning can uncover new mathematical structures in fluid dynamics. Focusing on equations such as the CCF, IPM and Boussinesq systems, Prof. Gómez-Serrano shows how carefully designed neural architectures, combined with high-precision optimisation, can construct previously unknown unstable singularities.

These solutions achieve striking levels of accuracy—approaching the limits of machine precision, constrained only by numerical round-off—and significantly surpass previous results. The approach combines curated machine learning methods with Gauss–Newton optimisation to navigate highly complex solution spaces. By pushing numerical methods to their limits, Prof. Gómez-Serrano argues this work opens the possibility of rigorous, computer-assisted proofs and offers a glimpse of how AI may transform the practice of theoretical mathematics and physics.

### Event information
This event, part of our AI for Mathematical Sciences series, takes place at 2 pm on Thursday 23 April at the London Institute for Mathematical Sciences, on the second floor of the Royal Institution. AIMS is sponsored by Nebius. This series is organised by LIMS fellows [Prof. Yang-Hui He](https://lims.ac.uk/yang-hui-he/) and [Dr Evgeny Sobko](https://lims.ac.uk/evgeny-sobko/). To register for the series please fill out the [online form](https://applications.lims.ac.uk/subscribe-to-aims).

Javier Gómez-Serrano shows how machine learning uncovers unstable singularities in fluid dynamics equations, achieving near-maximal accuracy.

Unstable singularities

Discovery of unstable singularities

Topological orders appear in mathematical physics, condensed matter and quantum information. Weicheng Ye examines how anomalous symmetry actions constrain their physical realisations. He formalises anomalies as lifting obstructions in algebraic topology, develops diagrammatic methods to compute them and shows how anomaly matching determines whether a topological order can arise in lattice models or quantum field theory.

[Dr Weicheng Ye](https://scholar.google.com/citations?user=sUNQUA0AAAAJ&hl=zh-CN) is a postdoc at the University of British Columbia. He completed his PhD at the Perimeter Institute and works on the mathematical structures underlying quantum field theory, with a particular interest in topological phases of matter, symmetry, and quantum anomalies.

Quantum London Seminar Series: this seminar is part of a joint seminar series organised by Matthew Buican at Queen Mary University of London and Juven Wang, Ben Delo Fellow at LIMS.

Weicheng Ye presents a framework for anomalies in topological orders and shows how they determine which phases can be physically realised.

Topological anomalies

Anomalies in topological orders: from algebraic topology to physical realisations

Dr Matthew Yu presents a unified categorical framework for gauging continuous and finite symmetries in arbitrary dimensions. It identifies electric and magnetic symmetries of G-gauge theory and captures symmetry breaking by charged matter. Using geometric categories, he extends equivariantisation to continuous groups and constructs a functorial Symmetry Topological Field Theory with boundaries, computing endomorphisms.

[Dr Matthew Yu](https://www.maths.ox.ac.uk/people/matthew.yu) is a postdoc in mathematical physics at Oxford University. He holds a PhD from the Perimeter Institute, where he studied topological phases using higher category theory and cobordism. His research interests encompass homotopical methods in quantum field theory.

Quantum London Seminar Series: this seminar is part of a joint seminar series organised by Matthew Buican at Queen Mary University of London and Juven Wang, Ben Delo Fellow at LIMS.

Matthew Yu introduces a categorical framework for gauging symmetries and constructs Symmetry Topological Field Theories with boundaries.

Continuous gauging

Geometric categories for continuous gauging

Topological quantum field theories (TQFTs) in 2+1 dimensions describe gapped phases supporting anyons, with a successful formulation in terms of modular tensor categories. However, this framework relies on spacetime orientability. Ippo Orii surveys current efforts to extend TQFTs to non-orientable manifolds—which are closely tied to time-reversal symmetry— and highlights key physical insights guiding their construction. 

[Ippo Orii](https://sites.google.com/g.ecc.u-tokyo.ac.jp/ippoorii/about) is a graduate student in theoretical physics at the Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo. His research focuses on topological quantum field theory, with interests in symmetry, anomalies and non-orientable manifolds.

Quantum London Seminar Series: this seminar is part of a joint seminar series organised by Matthew Buican at Queen Mary University of London and Juven Wang, Ben Delo Fellow at LIMS.

Ippo Orii surveys topological field theories and discusses the implications of recent progress in extending them to non-orientable manifolds.

Non-orientable TQFTs

 Insights from the crosscap state towards non-orientable TQFTs

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 real-world 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 to determine which AI search strategies are best suited for their own research.

## Event information
This event, part of our AI for Mathematical Sciences series, takes place at 2 pm on Thursday 2 April at the London Institute for Mathematical Sciences, on the second floor of the Royal Institution. AIMS is sponsored by Nebius. This series is organised by LIMS fellows [Prof. Yang-Hui He](https://lims.ac.uk/yang-hui-he/) and [Dr Evgeny Sobko](https://lims.ac.uk/evgeny-sobko/). To register for the series please fill out the [online form](https://applications.lims.ac.uk/subscribe-to-aims). 

Adam Zsolt Wagner discusses how AI-driven search in language space accelerates mathematical discovery and progress on long-standing problems.

New maths with AI

Searching in language space to find constructions in mathematics

A century after the Austrian theoretical physicist Erwin Schrödinger published his famous quantum wave equation, the exponential complexity of quantum many-body systems remains one of the central challenges of physics. In this lecture, Prof. Frank Verstraete presents how entanglement theory breaks this impasse through the development of tensor networks. He explains how these methods provide a powerful framework for efficiently representing and simulating strongly correlated matter, turning seemingly intractable problems into structured, computable ones.

Prof. Verstraete also demonstrates how such tensor networks reveal the organising role of quantum entanglement and make it possible to uncover emergent and generalised symmetries. These symmetries, in turn, define and classify quantum phases of matter. By combining conceptual insight with computational power, he argues that tensor networks now form an essential toolkit for understanding complex quantum systems.

## Event information
This event takes place at 4:30pm on Wednesday 4 March in the Faraday seminar room of the London Institute for Mathematical Sciences, on the second floor of the Royal Institution. Afterwards, there are drinks with the speaker in the Old Post room. LIMS colloquia are sponsored by Cognia.

Frank Verstraete shows how tensor networks harness entanglement to simulate strongly correlated quantum matter and reveal hidden symmetries.

Entanglement matters

Entanglement as an organising principle of quantum matter

This first talk in the AI for Mathematical Sciences (AIMS) seminar series features Prof. Kevin Buzzard, who presents the rapid rise of formalised mathematics in computer theorem provers such as Lean. Over the past decade, mathematicians have begun encoding proofs in precise formal languages that machines can verify line by line, eliminating ambiguity and ensuring complete logical rigour. In these systems, proofs can be checked automatically, helping to create durable, searchable libraries of trusted results and transforming how mathematicians collaborate and build on one another’s work.

Prof. Buzzard discusses the motivations of this movement, the technical bottlenecks that remain, and the growing role of AI tools that can write Lean code and help verify the output of large language models. He also reflects on leading a major project to formalise a 21st-century proof of Fermat’s Last Theorem, and what such ambitious efforts signal for the future of mathematical research.

## Event information
This event, part of our AI for Mathematical Sciences series, takes place at 2 pm on Monday 9 March at the London Institute for Mathematical Sciences, on the second floor of the Royal Institution. AIMS is sponsored by Nebius. This series is organised by LIMS fellows [Prof. Yang-Hui He](https://lims.ac.uk/yang-hui-he/) and [Dr Evgeny Sobko](https://lims.ac.uk/evgeny-sobko/). To register for the series please fill out the [online form](https://applications.lims.ac.uk/subscribe-to-aims). 

Kevin Buzzard opens AIMS with his views on what a new era of formalised maths, Lean and AI—verified proofs mean for the future of research.

Formal proofs with AI

AI and the formalisation of mathematics

Shu-Heng Shao discusses conformal twist defects in 4d Maxwell theory, where electric and magnetic fields exchange roles. He determines their operator spectrum by solving classical wave equations with twisted boundary conditions and shows that defect correlation functions split into universal and chiral current sectors. He also revisits related 2d defects and explores a ’t Hooft anomaly and its dynamical implications.

[Dr Shu-Heng Shao](https://physics.mit.edu/faculty/shu-heng-shao/) is a theoretical physicist at MIT. His research explores structural aspects of quantum field theories and lattice systems, with a focus on non-invertible symmetries, which appear in quantum systems such as the Ising model, Yang-Mills theories and the Standard Model.

Shu-Heng Shao analyses twist defects in 4d Maxwell theory, deriving their operator spectrum and a chiral sector from classical wave equations.

Cosmic string duality

Cosmic string for electromagnetic duality

Energy conditions are central assumptions in classical general relativity, where they place bounds on the stress–energy tensor and underpin key results such as the singularity theorems. Quantum theory complicates this picture: quantum fields admit states with locally negative energy density, violating classical energy conditions. These violations are not arbitrary, however, and are constrained by quantum energy inequalities that limit their size and duration.

In this course, Dr Eleni Kontou reviews the classical energy conditions, their physical motivation, and the ways in which they can fail in realistic settings. She introduces quantum field theory on curved spacetimes and explains how quantum energy inequalities arise from first principles. The course then explores the average null energy condition in detail, examining the restrictions it places on exotic spacetimes and the implications for causality, spacetime structure, and the foundations of gravitational theory.

## Event information
This is a four-part lecture series from LonTI Lectures are on Mondays at 10:30 am in the seminar room at the London Institute, on the second floor of the Royal Institution, followed by drinks and snacks onsite. To register and attend, please visit [LonTI website](https://lonti.weebly.com/).

Eleni Kontou explores energy conditions in classical general relativity and QFT, showing how quantum bounds constrain negative energy.

Quantum energy bounds

Classical and quantum energy conditions

Symmetry Topological Field Theory (SymTFT) enables the systematic exploration of quantum systems with generalised symmetries. Alison Warman outlines the framework of the theory and and its application to phases of matter, including gapped phases where symmetry-broken vacua carry distinct forms of topological order.  She also shows how SymTFT techniques can be used to construct Clifford-hierarchy quantum computing phase gates in 2D.

[Alison Warman](https://www.maths.ox.ac.uk/people/alison.warman) is a PhD student at Oxford University, where her doctoral research is supervised by Prof. Sakura Schäfer-Nameki. Her work focuses on generalised symmetries in fundamental quantum systems, ranging from high energy physics to condensed matter and quantum computation. 

Alison Warman explains how Symmetry Topological Field Theory classifies quantum phases and informs advances in quantum information research.

Phases and phase gates

The London Institute welcomes invited guests to an evening of piano music for four hands with the Ukrainian brothers Alexei and Sasha Grynyuk, acclaimed concert pianists whose close partnership brings this repertoire vividly to life. During the interval, Prof. Yang-Hui He offers a short mathematical interlude, reflecting on pattern and variation in music.

Johannes Brahms’ *Variations on a Theme by Robert Schumann* arise from one of the most human stories of the Romantic era. Welcomed by Robert and Clara Schumann in the early 1850s, Brahms was profoundly shaped by their circle. The variations carry something of that private world into the concert hall.

Franz Schubert’s *Variations on an Original Theme in A-flat Major* come from Vienna’s rich culture of domestic music-making. Heard together, the works trace a Romantic fascination with how a single idea can be transformed. The antique Steinway & Sons grand piano heard this evening is generously on loan from Sasha Grynyuk.

## Event information
The event takes place on Friday 13 February at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. Attendance is by invitation only. Arrival is from 5 pm in the Old Post Room. The concert, which will be held in Faraday’s Study, begins at 6 pm and will be followed by drinks with the musicians into the evening.

The Grynyuk brothers perform piano music for four hands by Brahms and Schubert, with a mathematical interlude by LIMS Fellow Yang-Hui He.

Piano and patterns

Performers

In *The Road to Reality* and *Fashion, Faith and Fantasy*, theoretical physicist Roger Penrose criticises string theory from conceptual, technical and methodological perspectives, alongside sociological reflections on the string theory community. In this talk, Dr James Read assesses Penrose’s conceptual and technical criticisms, focusing on objections that invoke the idea of functional freedom and their implications.

[Dr James Read](https://www.philosophy.ox.ac.uk/people/james-read) is a philosopher of physics at Oxford University. His research focuses on the foundations of spacetime theories such as general relativity, as well as scrutinising what some of physicists’ best theories, including quantum mechanics, say about the nature of reality.

Philosopher James Read explores how ideas of functional freedom shape the renowned mathematician Roger Penrose’s critique of string theory.

Functional freedom

On functional freedom and Penrose's critiques of string theory

This 14-week course examines how artificial intelligence can be integrated into contemporary mathematical research. More than a general overview of AI, it focuses on concrete applications in mathematical discovery, drawing on recent research papers and hands-on coding exercises.

The course covers training and deploying models, as well as using algorithmic optimisation and reinforcement learning to search for proofs, examples and counterexamples. Participants also learn to use AI-assisted coding to design computational experiments and build reasoning tools that function as research companions.

The course is developed by Nebius, a global AI infrastructure company that assists Microsoft, Meta and Cursor in training and deploying frontier models at scale. One key focus of Nebius’s research programme is AI for mathematics, including collaborations with the Stevens Institute of Technology and Caltech, and support for the London Institute’s new AI in Mathematical Sciences seminars.

## Event information
This is a 14-week course. Seminars are on Wednesdays at 10am in the seminar room at the London Institute, on the second floor of the Royal Institution, and conclude at 1 pm, with a break for coffee and tea. To register and attend, please visit the [Nebius Academy website](https://academy.nebius.com/ai-for-math).

The London Institute hosts a 14-week course by Nebius Academy on using AI to explore ideas and generate and test conjectures in mathematics.

Learn AI for maths

Simon Norton, who died in February 2019, is best remembered by mathematicians for his remarkable contributions to group theory. A child prodigy, Norton earned a First in mathematics from the University of London while he was still studying at Eton College.

Later, at Cambridge University, he collaborated with John Conway on several influential projects, co-authoring a landmark paper on monstrous moonshine. Published in 1979, the paper proposed a deep connection between the monster group and the *j*-function. The seemingly far-fetched conjecture was proved in 1992 by Richard Borcherds and is now recognised as one of the great unifying conjectures in modern mathematics.

Simon was also an important contributor to the five-author ATLAS of Finite Groups—a definitive catalogue of symmetry types, containing essential information on the sporadic simple groups and the smaller members of the infinite families. In the third Simon Norton Lecture, Prof. Robert Curtis discusses Simon’s involvement in the ATLAS from its inception to its publication, explaining the crucial role finite groups play across mathematics and science.

## Event information 
The event takes place on Thursday 5 March at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. To book a place, email smc@lims.ac.uk.

## Programme
- *5:30pm* Arrival and drinks, Old Post Room.
- *6:00pm* Prof. Yang-Hui He, Introduction, Tyndall seminar room.
- *6:10pm* Prof. Robert Curtis, “Simon Norton and the ATLAS of Finite Groups”
- *7:10pm* Drinks and canapes, Old Post room

In the third Simon Norton Lecture, Robert Curtis will describe Simon’s pivotal contributions to the classic ATLAS of Finite Groups.

Simon and the ATLAS

The London Institute was founded in 2011 and incorporated on 10 February. This marked the birth of Britain’s only independent research organisation in the physical sciences. The date is also the feast day of St Scholastica, who lived in Italy in the 6th century and is the patron saint of learning and Benedictine nuns.

One of the few surviving stories about St Scholastica is that one night, after her brother St Benedict had dined with her, he rose to leave. She prayed to God to make it rain, so he would be compelled to stay and they might continue talking. So it came to pass. St Scholastica is therefore indelibly associated with evenings filled with good conversations, which continue into the night.

To celebrate our founding and our belief in the value of community, we hold an annual St Scholastica’s Feast in our rooms. This formal dinner is for our scientists and staff and a handful of distinguished guests. It takes place on a Friday near the day of our incorporation.

## Event information
The dinner is at 7 pm on Friday, 27 February in our rooms on the second floor of the Royal Institution. Dress is black tie. We meet in the Old Post Room, then head to dinner in the Faraday Room and dessert in the Bragg Room, followed by drinks in the Old Post Room.


We hold an annual formal dinner in our rooms, to mark the anniversary of our founding and affirm our belief in the importance of community.

St Scholastica’s Feast

The product replacement algorithm generates random elements of a finite group, yet performs far better than theory predicts. A key parameter is the largest size of a minimal generating set. In this talk, building on Julius Whiston’s result that the symmetric group on n points has size n–1, Prof. Colva Roney-Dougal presents new tight bounds for all its subgroups and explores their wider impact on product replacement.

[Colva Roney-Dougal](https://research-portal.st-andrews.ac.uk/en/persons/colva-roney-dougal/) is a professor of pure mathematics at St Andrews. She holds a PhD from Queen Mary University of London and is also known for her work on popularising mathematics, particularly on the radio. Her research focuses on group theory and computational algebra.

Colva Roney-Dougal gives new bounds on minimal generating sets in permutation groups and shows what they reveal about product replacement.

Permutation group limits

Minimal generating sets of permutation groups

Gauge theories play an essential role both in condensed matter and high-energy physics. Topological gauge theories also have mathematical applications, as they provide invariants of manifolds. Dr Pavel Putrov explores the relationships between gauge theories with finite and continuous gauge groups that have the same underlying algebraic group, considered over a finite field and over complex numbers, respectively.

[Dr Pavel Putrov](https://www.ictp.it/member/pavel-putrov#biography) is a research scientist at ICTP. He did his PhD in theoretical physics at the University of Geneva. He was the Sherman Fairchild Prize Postdoctoral Fellow at Caltech and a postdoc at the IAS. His work focuses on mathematical aspects of quantum field theories.

Pavel Putrov explores surprising connections between 3D topological gauge theories based on finite groups and their continuous counterparts.

Finite vs continuous

A relationship between gauge theories with finite and continuous gauge groups

In its ninth iteration, String Data 2025 brings together leading theorists, mathematicians and computer scientists for three days to discuss how open problems in theoretical physics can be addressed through the use of techniques from computer science. Held jointly this year at the Infosys Centre and the London Institute for Mathematical Sciences, the programme features keynote talks, presentations, poster sessions and panel discussions.

Participants examine how machine learning and data science can shed light on deep problems such as the structure of the string landscape, the dynamics of quantum fields and the geometry underpinning fundamental theory. With speakers drawn from top institutions worldwide, the event aims to build new bridges between disciplines and spark breakthroughs in foundational physics.

This year’s programme also includes, on Tuesday, a public-facing talk and panel on the parallels between the neural networks underlying AI and quantum field theory.

## Event information
This conference takes place from Monday 8 to Wednesday 10 December.  On Tuesday 9 December the event will be hosted by the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution in Mayfair. On other days, the event will take place at the Infosys Centre. For further details, please visit the conference [website](https://indico.global/event/14913/overview).

The London Institute co-hosts the leading international conference at the intersection of string theory, data science and machine learning.

String Data 2025

Far more than other nations such as Germany and America, Britain suffers from a dearth of independent institutes. That means that the lion’s share of our research takes place at universities, where all too often scientists must divide their time between research, teaching and administrative duties. 

In this event, the Tony Blair Institute will unveil its vision for a new kind of research organisation. The Lovelace disruptive invention laboratories will offer an alternative model, which is designed to pursue ambitious, high-risk ideas with long-term vision.  Characteristics that will set them apart from universities include the offer of early-career independence for scientists, a reliance on internal review as opposed to chasing grants, and directors with genuine autonomy. Partly inspired by the example set by the London Institute, the labs aim to accelerate discovery, attract world-class talent and bridge the gap between fundamental discovery and marketable innovation. 

## Event information
The event takes place on Thursday 20 November at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. Attendance is by invitation only. There will be speeches from 7 pm in our seminar room, followed by drinks in the Old Post Room.

The Tony Blair Institute unveils its vision for a new kind of research institution to policymakers and the press at the London Institute.

Launching Lovelace labs

_tex: In 1936, Bartel van der Waerden predicted that among all monic integer polynomials of degree $n$ with absolute values of coefficients at most $H$, only about $O(H^{n-1})$ fail to have the full symmetric Galois group. This had been proved only for degrees up to four, through work by van der Waerden and later Sam Chow and Rainer Dietmann. In this seminar, Prof. Manjul Bhargava presents a proof of the conjectured bound in all degrees, showing that polynomials of large degree with smaller-than-expected Galois groups form only a thin exceptional set.

## Event information
The seminar, which will be held in the Faraday room, starts at 3 pm and is followed by a Q&A.

In this seminar, Fields Medalist Manjul Bhargava proves the van der Waerden conjecture on counting polynomials with small Galois groups.

Van der Waerden proven

Galois groups of random polynomials

Algebraic geometry has always been an intrinsically interdisciplinary subject, shaped by ideas from algebra, geometry, physics and number theory. Yet genuinely collaborative work requires more than shared interests: it demands that researchers gain a clear view of one another’s methods, motivations and results.

This workshop brings together graduate students and early-career mathematicians to foster exactly that exchange. Participants prepare and deliver research talks, present papers, and learn to navigate unfamiliar areas through the talks of their peers. The meeting blends research and education in a focused, supportive environment, allowing young algebraic geometers to broaden their technical range, sharpen their communication skills, and engage deeply with neighbouring subfields. By the end, they not only strengthen their understanding of algebraic geometry’s many facets but also build the relationships and shared vocabulary needed to begin new collaborative projects.

## Event information
This workshop takes place on Wednesday 26 November at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution in Mayfair. To register to attend this workshop, please visit the [conference website](https://sites.google.com/view/agworkshopforphd).

The London Institute hosts a workshop on algebraic geometry for PhD students to share their research results and initiate collaborations.

Arrival

In this talk we observe that the categorical structure of a flop occurs for some well-known non-commutative resolutions of a nodal curve. We describe the flop-flop spherical twists, and give a geometric interpretation in terms of Landau–Ginzburg models. The resolutions are all weakly crepant but not strongly crepant, and we formulate an intermediate condition that distinguishes the smaller ones.

A categorical flop in dimension one

In this talk, we prove Homological Mirror Symmetry for the family of hypersurfaces in P(1, 1, 1, k). We construct an explicit mirror map, as well as a new construction exhibiting the special McKay correspondence on the A-side.

A Homological mirror symmetry for some orbifold Del Pezzo surfaces 

We demonstrate some unexpected properties that simple gluings of the simplest derived categories may have. We consider two special cases: the first is an augmented curve; the second is an ideal point gluing of curves. We construct unexpected exceptional objects contained in these categories and discuss their orthogonal complements.

Compact type generations of curves

Lunch

In this talk we discuss how generalised Kummer varieties degenerate to natural symplectic subvarieties of the Hitchin system for curves with genus larger than 2. Given a closed immersion between arbitrary smooth complex projective varieties one can take the deformation to the normal cone family. For curves in symplectic surfaces, the corresponding deformation to the normal cone space is an open subset of the relative moduli space of sheaves. 

Moduli of Sheaves and Deformation to the Normal Cone

In this talk we will describe Gopakumar–Vafa (GV) invariants associated to cAn singularities. This involves generalising GV invariants to crepant partial resolutions of cAn singularities, and showing that they satisfy Toda’s formula. We then study filtration structures on the parameter space of contraction algebras associated to cAn crepant resolutions and, finally, numerically constrain the possible tuples of GV invariants that can arise. 

GV invariants associated to cAn singularities

The notion of categorical absorption of singularities will be introduced. This is an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper category. For a projective variety X with isolated ordinary double points categorical absorption will be described.

Categorical absorptions of singularities and degenerations

Algebraic exchange

Workshop on algebraic geometry

Edward Frenkel is a professor of mathematics at UC Berkeley, a member of the American Academy of Arts and Sciences and winner of the Hermann Weyl Prize. He is also the author of *Love and Math*—part memoir, part masterclass in mathematical storytelling—which became a *New York Times* bestseller and has been published in 20 languages.

In this event, Prof. Frenkel joins London Institute Fellow Yang-Hui He and our chief science writer Ananyo Bhattacharya to reflect on his intellectual journey and tackle some of the most pressing questions in mathematics today. How can researchers argue for the value of basic science in a world of competing priorities? Will AI one day make human mathematicians obsolete?

The evening also offers a rare chance to hear an insider’s take on the Langlands programme—sometimes called the “grand unified theory of mathematics”—famed for its depth, difficulty and breathtaking beauty.

There will be time for audience questions and discussion over drinks.

## Event information
The event is on Friday 12 December at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. Entry is by invitation only. The interview starts at 5:30pm in our Faraday seminar room, followed by a Q&A at 6:30pm. Afterwards there are drinks with the speaker into the evening, in the Faraday and Old Post rooms.

Edward Frenkel charts his path from Moscow to Berkeley and the quest for a unified theory of maths with the London Institute and its guests.

Meet Edward Frenkel

Prof. Manjul Bhargava is one of the foremost mathematicians of our time. His pioneering work in number theory has reshaped the geometry of numbers and earned him the Fields Medal, mathematics’ highest honour. A passionate advocate of India’s mathematical past and future, he also holds positions at the Tata Institute of Fundamental Research and other leading Indian institutions. Beyond mathematics, he is a scholar of Sanskrit and an accomplished tabla player.

At this reception in his honour, Prof. Bhargava discusses the promise of Indian mathematics and the urgency of supporting it. Dr Thomas Fink, Director of the London Institute, will describe our Ramanujan Junior Fellowships scheme, which will bring exceptional young Indian theoretical physicists and mathematicians to the London Institute for three transformative years.

The London Institute is  seeking visionary supporters to help realise this programme and strengthen our mission to advance fundamental research.

## Event information
The event takes place on Tuesday 25 November at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. The event is limited to 80 people and is by invitation only. There will be speeches at 6pm in our Faraday seminar room, followed by drinks with the speaker into the evening.

We hail India’s elite mathematical talent—and our Ramanujan Junior Fellowships scheme to nurture it—with Fields Medalist Manjul Bhargava.

Meet Manjul Bhargava

[Prof. Daniel Jafferis](https://www.physics.harvard.edu/people/facpages/jafferis) reviews a tensor–matrix model for 2d CFT data constrained by crossing symmetry, and topological expansion conjectured to match pure 3d gravity. He discusses sources of divergences and what remains to establish the duality, then turns to a BCFT extension linked to an open bootstrap. The resulting expansion corresponds to gluing tetrahedra, with the model reproducing certain 3d gravity amplitudes.

Prof. Daniel Jafferis is a physicist at Harvard University. He co-discovered key AdS/CFT dualities and proposed the F-theorem for 3D supersymmetric flows. Prof. Jafferis’s works on tensor–matrix models, holography and the unexpected links between mathematics, geometry and gravity.

Daniel Jafferis outlines a tensor–matrix model constrained by crossing, its proposed gravity dual and a BCFT version encoding amplitude data.

Tensor–matrix gravity

Tensor models, 3d gravity and simplicial decomposition

Prof. Dmitry Kaledin gives two lectures on the frontiers of modern algebraic geometry. In the first, he explores how classical Hodge theory extends—or fails to extend—to the non-commutative realm. In non-commutative geometry, de Rham cohomology is replaced by periodic cyclic homology, yet many foundational questions remain unresolved and there is no general theory over the complex numbers. Prof. Kaledin outlines a potential new framework for constructing a genuine non-commutative Hodge theory, building on insights from p-adic and crystalline settings and revealing unexpected connections between geometry and arithmetic.

In his second lecture, he presents a general approach to building a homotopically
enhanced category theory, based on Alexander Grothendieck’s idea of a “derivator”. This work aims to make abstract structures more flexible and computationally powerful, offering practical tools for researchers working across geometry, topology and mathematical physics.

## Event information

The first lecture, at 1:00 pm on Monday, 24 November, is part of the MAGIC algebraic geometry seminar series and will take place at Imperial College. The second is at 3:00 pm on Friday, 28 November and will take place in the seminar room of the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. 

In two lectures, Dmitry Kaledin explores progress towards a non-commutative Hodge theory and a theory of homotopically enhanced categories.

Homotopy & categories

Non-commutative Hodge theory and enhancing categories

Prof. Ran Tessler explores how the amplituhedron offers a geometric framework to understand the surprising connections between scattering amplitudes in N=4 Super Yang–Mills theory and cluster algebras. These links are not only conceptually rich but also essential for practical amplitude calculations. He presents a key cluster relation, its proof, and a new conjectural generalisation expressed in the language of operads.

[Prof. Ran Tessler](https://www.weizmann.ac.il/math/tessler/home) is a mathematician at the Weizmann Institute whose work bridges geometry, combinatorics and physics. He studies scattering amplitudes, amplituhedra and their links to cluster algebras, exploring the deep structures that connect mathematics and quantum theory.

Ran Tessler reveals how the amplituhedron connects quantum field scattering amplitudes to cluster algebras through geometry and symmetry.

Geometry of amplitudes

Amplituhedra and cluster structures on scattering amplitudes

Dr Brandon Rayhaun shows how the irreversibility of renormalisation group flow, combined with anomalies—including those in the space of coupling constants—can be used to constrain the infrared phases of defects in well-known quantum field theories. As an illustration, he presents new evidence for a conjectural “spin–flux duality”, which describes how line operators map across particle–vortex duality in 2+1 dimensions.

[Dr Brandon Rayhaun](https://www.ias.edu/scholars/brandon-rayhaun) is a Leinweber Physics Member at the Institute for Advanced Study. He did his PhD at Stanford. He works on problems at the interface of high energy theory, condensed matter physics and pure mathematics, using quantum field theory and string theory as frameworks.

Brandon Rayhaun examines the long-distance physics of defects in QFTs through anomalies and the irreversibility of renormalisation flow.

Defects and duality

Anomalies of defect parameter spaces and a spin-flux duality

When Richard Feynman died in 1988, his last blackboard bore a curious note to himself: “To learn: Bethe Ansatz.” The Bethe Ansatz, introduced by Hans Bethe in 1931, is a method for finding the spectra of Hamiltonians in quantum integrable systems such as the Heisenberg magnet. For decades it helped produce astonishing results and conjectures, though no one quite knew why it worked.

In this talk, Prof. Edward Frenkel revisits this enduring mystery. In collaboration with Boris Feigin and Nicolai Reshetikhin, he reinterpreted the Bethe Ansatz through the lens of the geometric Langlands correspondence, expressing its spectra in terms of mathematical objects known as opers. This framework led to powerful generalisations involving q-characters of quantum affine algebras and q-opers, bridging quantum physics and modern geometry.

Prof. Frenkel explores these ideas and reflects on why the Bethe Ansatz—an old key to new symmetries—still stood at the top of Feynman’s list.

## Event information
The event takes place on Thursday 11 December at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution.

Edward Frenkel illuminates Feynman’s final quest—to learn the Bethe Ansatz—with fresh insights from the geometric Langlands correspondence.

Feynman’s last wish

Quantum integrable systems: from Bethe Ansatz to Langlands duality

By analytically studying the repeated composition of simple Boolean functions, Dr Thomas Fink uncovers the spontaneous emergence of a law of parsimony. It is the first exact solution of a nontrivial input-output map, and suggests an explanation for why neural networks are biased towards simplicity in the models that they generate. The general result applies whenever composition of more than one input occurs.

[Dr Thomas Fink](https://lims.ac.uk/thomas-fink/) is the founding Director of the London Institute and Charge de Recherche in the French CNRS. He studied physics at Caltech, Cambridge and École Normale Supérieure. His work includes statistical physics, combinatorics and the mathematics of evolvable systems.

Our director Thomas Fink explains why the repeated application of simple logics induces a bias towards simplicity, with applications to AI.

Why AI works

Why AI works: The spontaneous emergence of a law of parsimony

To many, science appears as a kind of modern magic—the only magic that works. In the Soviet Union, an officially atheist state, science was elevated even further, becoming a substitute for religion.  The DAU project began as a biopic of Lev Landau, the Nobel Prize–winning physicist and icon of Soviet science. But it evolved into something far more ambitious: a vast social and artistic experiment exploring what it means to be Soviet, to be modern and to believe in science. 

As part of the project, hundreds of participants lived and worked inside a reconstructed Soviet research institute, their lives filmed in an unprecedented exploration of the scientific worldview. Among the works born of the ongoing project was *DAU. Natasha*, which won the Silver Bear at the Berlin International Film Festival in 2020.

In this talk, Prof. Dmitry Kaledin offers a rare insider’s view of DAU—from its portrayal of Soviet scientific culture to its deeper inquiry into the meaning of science itself.

## Event information
The event takes place on Thursday 27 November at the London Institute for Mathematical Sciences, which is on the second floor of the Royal Institution. To book a place, register [here](https://tally.so/r/3lokj6).


Dmitry Kaledin reflects on the DAU project—an audacious theatrical experiment probing science and belief in the Soviet Union and beyond.

The magic of DAU

DAU: the magic that works

Matter and fundamental forces are governed by non-abelian gauge theories and general relativity. These theories look very different, but recent research has uncovered the “double copy”—an exact correspondence between their mathematical structures. Prof. Chris White reviews its theoretical origins and practical uses, highlighting links to string theory, exotic field theories, and open questions in pure mathematics.

[Prof. Chris White](https://www.seresearch.qmul.ac.uk/cfp/people/cwhite/) is a theoretical physicist at Queen Mary University of London. He studied at the University of Cambridge, before holding positions in Amsterdam, Durham and Glasgow. His research focuses on theories of particle physics, and their relationship to gravity and beyond. 

Chris White traces the origins and impact of a remarkable new correspondence linking non-abelian gauge theories with general relativity.

The double copy

The double copy: new connections in physics and mathematics

Matrix models—systems in which randomness and algebraic structure meet—play a central role across theoretical physics and mathematics. Often seen as zero-dimensional analogues of field theories, they also lie at the heart of deep connections linking string theory, integrability, quantum gravity, Yang–Mills theory, combinatorics, geometry, and representation theory.

In this four-part lecture series, Dr Levkovich-Maslyuk provides a guided, pedagogical journey through the subject: starting with motivation and definitions, through reduction to eigenvalue form, to continuum limits and spectral curves, and finally to orthogonal polynomials, phase transitions, and links to two-dimensional gravity. Along the way he sketches the broader vista of loop equations, topological recursion, and integrability. The series offers both newcomers and seasoned theorists a unified and illuminating view of how matrix models continue to shape modern research.

## Event information

This is a four-part lecture series from LonTI. Lectures are on Mondays at 10:30 am in the seminar room at the London Institute, on the second floor of the Royal Institution, followed by drinks and snacks onsite. To register and attend, please visit lonti.weebly.com.

Fedor Levkovich-Maslyuk traces how matrix models reveal striking connections between quantum gravity, string theory and integrability.

Can one hear the shape of a black hole singularity?

4:30PM, 21 Oct 2026

Event information

Speakers