The London Institute for Mathematical Sciences

Prof. Joseph Conlon explains how string theory suggests new equations of state that may describe the physics of the very early universe.

Early universe strings

Mikhail Burtsev explains how artificial intelligence is helping to decipher genomes in the Royal Institution’s iconic lecture theatre.

Decoding life with AI

Dr Matthew Buican explains how a universal deformation takes 3d N=4 superconformal field theories to 3d topological quantum field theories.

Conformal to topological

We have simplified our soft power page, which now comprises voice, website, building, meetings, recruitment and organisational intelligence.

Soft power revised

Simon Telen presents his discovery of a new connection between polynomials inspired by particle physics and classical algebraic geometry.

Geometry meets physics

We’ve added horizontal scrolling to our website, providing a cleaner way to visualise and navigate evolvable scripts, such as our rituals.

Horizontal scrolling

The Journal Physics Letters B accepts the paper “BPS spectroscopy with reinforcement learning” by our Fellow Yang-Hui He and coauthors.

Reinforcing spectra

Antoine Pinardin presents a complete description of the linearisable subgroups of the plane Cremona group over the field of complex numbers.

Linearising groups

In The Times, our writer Thomas W. Hodgkinson reviews a compelling history of the “like” button, co-written by our Trustee Martin Reeves.

Liking the like?

Florian Schuster is a LIMS Trustee. An investor and entrepreneur, he advises on financial strategy, promotes our values and raises funding.

New Trustee

Quantum many-body systems share patterns of dynamics that are exactly described by tridiagonal matrices based on continuous Hahn polynomials.

On universal dynamics

We introduce an AI-based framework for finding solutions to the Yang-Baxter equation and discover hundreds of new integrable Hamiltonians.

Learning integrability

Dr Po-Shen Hsin introduces generalised symmetries in quantum systems and explores their roles in dynamics, constraints and applications.

Quantum symmetries

Juven Wang is the Ben Delo Fellow at LIMS. Previously a Fellow, he took up the prestigious new post that was created by a gift from Ben Delo.

Ben Delo Fellow

In a time of government cuts to mathematics, the entrepreneur and philanthropist Ben Delo explains why he’s funding a new Fellowship at LIMS.

My passion for maths

We show reinforcement learning can be used to check whether a certain class of quantum field theory has a finite spectrum of stable particles.

Mathematicians across London share their work on the formalisation of mathematics using the AI proof-assistant computer language Lean.

London learns Lean

Prof. Konstantinos Zoubos will use Lie groupoids and their twists to uncover hidden symmetries of supersymmetric orbifold field theories.

Groupoids do the twist

In two consecutive talks, Prof. Koji Hashimoto and Dr Akio Tomiya discuss applying machine learning to problems in quantum field theory.

AI for QFT

Dr Bhavik Mehta from Imperial College London gives an overview of Lean, the proof-assistant computer language used to formalize mathematics.

Co-piloting proofs

The Journal of Lie Theory accepts “Irreducible actions of the infinite-dimensional general linear group on...” by Oleksandr Kosyak and coauthor.

Irreducible group action

We use simulated annealing to efficiently construct all brane tilings that encode supersymmetric gauge theories and discover a new one.

Metaheuristic tilings

Dr Matthew Yu explains how fermionic topological quantum field theories can be given a categorical description in 3+1-dimensional spacetime.

Fermionic TQFTs

Dr Andrea Guerrieri explores QCD in two distinct regimes to illustrate its pivotal role in shaping our understanding of fundamental physics.

QCD’s IR and UV limits

Evgeny Sobko is a Fellow at LIMS. Previously a Landau Fellow, he took up the new post after a global competition for our new Fellowship.

LIMS Fellow

We achieve maximal-fidelity state transfer in the fastest possible time for a 3-qubit chain by applying the quantum variational method.

Three-qubit shortcut

Sterile neutrinos are replaced by topological order as dark matter candidates to counterbalance the Standard Model’s gravitational anomalies.

Topological dark matter

3-manifolds represented as isomorphism signatures of their triangulations and associated Pachner graphs are analysed with machine learning.

Learning 3-manifolds

The Journal Physics Letters B accepts the paper titled “Metaheuristic generation of brane tilings” by our Fellow Yang-Hui He and coauthors.

Continuous quivers enable exact Wilson loop calculation, reveal an emergent dimension, and raise tantalising questions on dual strings.

Continuous  quivers

The Journal of Physics: Complexity accepts “Network analysis of memristive device circuits: dynamics, ...” by Forest Sheldon and coauthors.

Circuits with memory

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 Journal of Physics A: Mathematical and Theoretical accepts “Learning 3-manifold triangulations” by Yang-Hui He and coauthors.

In the second Simon Norton Lecture, Prof. Leonard Soicher will convey the mystery and the magic of the monster group to a general audience.

A friendly monster

The Journal of Combinatorial Theory, Series A accepts the paper titled “On common energies and sumsets” by our Arnold Fellow Ilya Shkredov.

Common energies

The journal Physical Review D accepts the research paper entitled “Continuous quiver gauge theories” by our Landau fellow Evgeny Sobko.

Continuous quivers

The abilities and power of a type of transformer model with memory is greatly improved by learning several key tasks at once during training.

Multitasking  memory

We use the quantum brachistochrone method to design an optimal control strategy for the fastest quantum state transfer in long qubit chains.

Optimal transfer

Prof. Alexander Migdal presents an infinite dimensional manifold of exact solutions to the Navier-Stokes equations for decaying turbulence.

Solving Navier-Stokes

Dr Tarek Anous introduces the 50-year-old black hole information paradox and discusses some of the questions that have yet to be answered.

Black hole paradox

We study the geometry of finite dimensional space as the dimension grows to infinity with an accent on the height of the parallelotope.

Infinite parallelotope

A family of transformer-based DNA language models can interpret genomic sequences, opening new possibilities for complex biological research.

Speaking DNA

Dr Alex Davies of Google DeepMind leads an interactive discussion about AI-assisted mathematical discovery and automated theorem proving.

Automating maths

The journal Finite Fields and Their Applications accepts “On the distribution of quadratic residues” by our Arnold fellow Ilya Shkredov.

Quadratic residues

We propose that dark matter consists of topological order, so gapped anyon excitations decay to generate the Standard Model's lepton asymmetry.

A new leptogenesis

We demonstrate that the Standard Model's baryon minus lepton symmetry defect can become categorical by absorbing the gravitational anomaly.

Categorical symmetry

Charge conjugation C, space reflection R, and time-reversal T operators are regularised in a quantum many-body Hilbert space on a discrete lattice.

Regularising  CRT

The journal Nucleic Acids Research accepts “GENA-LM: a family of open-source foundational DNA language models for long...” by Mikhail Burtsev et al.

The dynamics of the Kauffman network can be expressed as a product of the dynamics of its disjoint loops, revealing a new algebraic structure.

Multiplicative loops

Modelling the behaviour of two interacting bosonic particles in a chiral, dimerized optical lattice shows the pair form a vortex bound state.

Vortex bound states

Varying the spacetime dimensions fermions occupy shows charge-conjugation C, space-reflection R and time-reversal T symmetries are 8-fold periodic.

An 8-fold way for CRT

We give a solution of the linearisation problem in the Cremona group of rank two over an algebraically closed field of characteristic zero.

Linearising actions

To secure its long-term future and attract world-class talent, LIMS is raising endowments for Chairs, Fellowships and Junior Fellowships.

Endowments

The journal Physical Review D accepts “Categorical symmetry of the standard model from gravitational anomaly” by Juven Wang and coauthor.

Charge-conjugation, space-parity and time-reversal symmetries are shown to form noncommutative groups, including the order-16 Pauli group.

C, P and T in fractions

Our Christmas party is an opportunity to celebrate our supporters and collaborators, review the past year, and set our plans for the future.

Christmas party

The journal Physical Review A accepts “Vortex bound states in dimerized flux optical lattices: Characterization...” by Andrei Stepanenko and coauthor.

The journal Physics Letters B accepts the paper “Generating triangulations and fibrations with reinforcement learning” by Yang-Hui He and coauthors.

Triangulating polytopes

A new approach to the large distance asymptotic of the finite-temperature deformation is discussed for a sine-kernel Fredholm determinant.  

Fredholm meets Toeplitz

Dr Juven Wang is a Fellow at LIMS. He explores many-body condensed matter, high-energy physics, quantum field theory, and quantum information.

Neural networks classify simple finite groups by generators, unlike earlier methods using Cayley tables, leading to a proven explicit criterion.

Learning to be Simple

The journal Linear Algebra and its Applications accepts the paper “The height of an infinite parallelotope is infinite” by Oleksandr Kosyak.

We show that Weyl fermions and anomalous topological order in 4 dimensions can live on the edge of the same 5-dimensional superconductor.

Topological boundary

The journal Communications in Mathematical Physics accepts “Reflexions on Mahler: Dessins, modularity and Gauge theories” by Yang-Hui He and coauthors.

Reflexions on Mahler

Mikhail Khodorkovsky talks to Thomas W. Hodgkinson about the future of Russia and why he supports Fellowships at the London Institute.

Re-ordering Russia

The London Institute, which uses humans to speed up fundamental discovery, launches Irix, a company that harnesses machines to do the same.

Launch of Irix

We compute Futaki invariants for gauge theories from D3-branes that probe toric Calabi-Yau singularities arising from reflexive polytopes.

Futaki for reflexives

The London Institute is recruiting an outstanding theoretical physicist or mathematician to take up an open-ended position, starting in 2025.

Like chess, theoretical research is an international game played in the language of patterns. Its intrinsic value transcends politics.

Science needs Russians

The London Institute is hiring Russian postdocs in physics and mathematics to join us, starting between 1 October 2024 and 1 October 2025.

Khodorkovsky Postdocs

The London Institute is hiring Russian and Ukrainian theorists to join us as fellows, starting between 1 October 2024 and 1 October 2025.

Arnold & Landau Fellows

Two approaches that provide local formulae for Compton amplitudes of higher-spin massive objects in the quantum regime and classical limit.

Spinning Root-Kerr

Nature Communications accepts “The backpropagation algorithm implemented on spiking neuromorphic hardware” by Forrest Sheldon and coauthors.

Spiky backpropagation

The additive dimension of a set, which is the size of a maximal dissociated subset, is closely connected to the rapid growth of higher sumsets.

Set additivity and grow

Why are physical insights from the real world proving so useful for solving abstruse problems in pure mathematics, Ananyo Bhattacharya asks.

From physics into maths

The London Institute is recruiting a new trustee to raise money, protect the Institute’s values, and enhance its profile on the global stage.

Trustee

Journal of High Energy Physics accepts “From higher-spin gauge interactions to Compton amplitudes for root-Kerr” by Alexander Ochirov et al.

In the Harvard Business Review, our trustee Martin Reeves and co-authors explain how ‘evolvable scripts’ greatly improve knowledge-sharing.

Spreading the word

Dr Juven Wang proposes novel solutions to open problems in high-energy phenomenology via new analogies from modern ultra quantum matter.

Ultra Unification

As a London Institute Trustee, the actress, author and tech entrepreneur Talulah Riley will support our mission to accelerate discovery.

Welcome, Talulah

Classical Kerr amplitudes for a rotating black hole derived using insights from recent advances in massive higher-spin quantum field theory.

Brightening black holes

A polynomial criterion is obtained for a set to have a small doubling, expressed in terms of the common additive energy of its subsets.

The Times’ science editor interviews our new Trustee, Talulah Riley, about her love of physics and her work with the London Institute.

Life of Riley

The abilities and power of a type of transformer model with memory are greatly improved by learning several key tasks at once during training.

Multitasking memory

Using Inception, a convolutional neural network, we predict certain divisibility invariants of Calabi-Yau manifolds with up to 90% accuracy.

Convolution in topology

The London Institute hosts a two-day workshop for theorists to discuss and explore the links between data science, AI and pure mathematics.

DANGER 2024

A review of progress in the nascent field of AI-assisted discovery in mathematics and theoretical physics identifies three main approaches.

On AI-driven discovery

Certain properties of the bivariate cubic equations used to prove Fermat’s last theorem exhibit flocking patterns, machine learning reveals.

Elliptical murmurations

The London Institute is recruiting a new governor to raise money, grow the Institute and support our start-ups that develop our discoveries.

Governor

In this seminar, Fields Medalist Caucher Birkar talks about sheaf stable pairs in algebraic geometry, especially for Fano varieties.

Stable pairs

Talulah Riley is a LIMS Trustee. An actress, author and tech entrepreneur, she helps us spread the gospel of curiosity driven science.

Inconsistencies between two approaches to deriving beta functions in two-dimensional sigma models are resolved by adding heavy superpartners.

Peculiar betas tamed

Experimental Mathematics accepts “Murmurations of elliptic curves,” by Yang He and coauthors, the first in a series of papers on the subject.

The London Institute’s vision is its fundamental purpose: “To use mathematics to discover the laws of the universe and our place within it.”

Our vision

Genetic symbolic regression methods reveal the relationship between amoebae from tropical geometry and the Mahler measure from number theory.

Analysing amoebae

The journal Physical Review Letters accepts “Compton amplitude for rotating black hole from QFT” by Alexander Ochirov and coauthors.

The journal Nature Reviews Physics accepts the perspective “AI-driven research in pure mathematics and theoretical physics” by Yang-Hui He.

We do curiosity-driven theoretical research. We build theories—concise mathematical descriptions of patterns—and identify their testable consequences. We pursue the most intriguing patterns, without concern for their usefulness, which leads to the most transformative breakthroughs.

Former Trustees