The London Institute for Mathematical Sciences

A link between the statistical properties of free fermions in one dimension when either half- or alternating- states are initially occupied.

Counting free fermions

Talking engages robust muscles of thought—not least when mathematicians take their problems to the blackboard, argues Thomas Hodgkinson.

Talking is thinking

The first exact solution for the vacuum state of an asymptotically free QFT in a general external field found for the Principal Chiral Model.

PCM in arbitrary fields

Our new soft power page catalogues all we do that doesn’t directly concern research and fundraising, such as our voice, website and building.

Soft power

Congratulations to Oleksandr Gamayun and coauthors, whose paper in Nature extends research on solitons that began in a 19th century canal.

Congratulations, Sasha

Nature has published the paper “Non-reciprocal topological solitons in active metamaterials” by Oleksandr Gamayun and coauthors.

Strange kinks

The advertising guru Graham Fink waxes lyrical about equations and working with the London Institute on the How Do You Feel Today? podcast.

Creative convergence

For its 225th birthday, our writer Thomas Hodgkinson hails the Royal Institution as proof of the vital importance of science communication.

Let's talk about science

The journal Physical Review Letters accepts “Large-N principal chiral model in arbitrary external fields” by Evgeny Sobko and coauthors.

Quanta reports on work by Yang-Hui He, who co-discovered unexpected patterns in a property related to the curves’ integer roots using AI.

Elliptic curve mystery

Following his popular Discourse, our Prof. Yang-Hui He and writer Madeleine Hall chat about the mysteries of geometry on the Ri Podcast.

Geometry’s dominion

Justine Crean is the assistant to the director at LIMS. She helps manage our scientists and staff and coordinate the Institute’s activities.

Assistant to the director

The London Institute is recruiting a world-class graphic designer to visualise our mathematical discoveries and enhance our visual identity.

Chief graphic designer

A Bloomberg piece names our Arnold and Landau Fellowships as one of the few programmes offering help to Russian and Ukrainian scientists.

Security and freedom

The journal Physical Review Research accepts the paper “Exact dynamics of the critical Kauffman model with connectivity one” by Thomas Fink.

Multiplicative loops

In the inaugural Simon Norton Lecture, Prof. Peter Cameron celebrates the mathematician's achievements and talks about Norton algebras.

A monstrous talent

We revised our content types page, which describes the building blocks of our site, and added new building blocks, such as jobs and rituals.

Content types

Researchers working on all aspects of gravity, from gravitational waves to black holes, discuss the latest developments in their field.

London Gravity Meeting

The London Institute recruited Arman Sarikyan as an Arnold Junior Fellow, one of a few we are recruiting this year. He starts on 1 July 2024.

A&L Junior Fellowships

The London Institute is hiring a full-time finance director to help us take our financial health and capacity for growth to the next level.

Finance director

Can AI do maths? In three separate publications, our scientists comment on the latest advances by the researchers at Google DeepMind.

AI at the Olympiad

Ananyo Bhattacharya is the chief science writer at LIMS. He writes about our research and our institute in the science and mainstream press.

Chief science writer

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

Our new Jobs page shows the jobs we are recruiting for and those we have filled, and introduces our standard template for job descriptions.

Jobs

The journal Nature accepts the paper “Non-reciprocal topological solitons in active metamaterials” by Oleksandr Gamayun and coauthors.

A transformation for spin and charge degrees of freedom in one-dimensional lattice systems allows direct access to the dynamical correlations.

Spin-charge separation

In a piece in Nautilus, our scientists talk about why they prefer the 1,000-year-old technology of blackboards to their digital equivalents.

The art of blackboards

In a Nature correspondence, our scientists argue that, by the terms of “the Birch test” no AI has yet made a genuine mathematical discovery.

A Birch for AI's back

The London Institute is hiring four outstanding young physicists and mathematicians from Russia, Ukraine and Belarus to join us in 2024.

The London Institute is recruiting two outstanding physicists and mathematicians in the early stages of their career to join us in 2024.

LIMS Junior Fellowships

Surprisingly, the number of attractors in the critical Kauffman model with connectivity one grows exponentially with the size of the network.

Kauffman cracked

Physical Review A accepts “Emergence of anyonic correlations from spin and charge dynamics in one dimension” by Oleksandr Gamayun et al.

It’s a mistake to credit large language models with human levels of reason and other abilities. To use them well, we must know their limits.

The limits of LLMs

The permanent revolution of AI means companies must do more than just adapt to the latest advance. They must become more adaptable.

It’s happening now

Explicit computation of injection and ejection impurity’s Green’s function reveals a generalisation of the Kubo-Martin-Schwinger relation. 

Mobile impurity

Effective field theories for Kerr black holes show that the 3-point Kerr amplitudes are uniquely predicted using higher-spin gauge symmetry.

Black hole symmetry

Our new Rituals page describes the processes and traditions that the London Institute has developed over the years, which form our culture.

Rituals

Physical Review Letters accepts “Number of attractors in the critical Kauffman model is exponential” by Thomas Fink and Forrest Sheldon.

Researchers working on all aspects of gravity, from gravitational waves to black holes, discuss recent developments in the field.

The luthier Robert Brewer Young explains the geometry of the violin, with musical accompaniment on two violins made by Stradivari himself.

Listening to maths

Dr Vyacheslav Lysov is our new Arnold Fellow. He works on tropical mirror symmetry, supersymmetric localisation and asymptotic symmetries.

Welcome, Vyacheslav

Our values are the fundamental organising principles of the London Institute. They determine what we do, how we do it, and who we recruit.

Values

Physical Review Letters accepts the paper “Kerr black holes from massive higher-spin gauge symmetry” by Alexander Ochirov and coauthors.

A new non-linear mechanical metamaterial can sustain topological solitons, robust solitary waves that could have exciting applications.

“Recursively divisible numbers” is accepted by the Journal of Number Theory, which introduces a recursive analog of the divisor function.

Recursively divisible numbers

Dr Evgeny Sobko is our new Landau Fellow. His research focuses on exactly solvable models in quantum field and string theory.

Welcome, Evgeny

Professional sport has a lot to teach scientists about pushing the limits of human achievement—so why are we still content to be amateurs?

Science goes pro

Dr Federico Carta is our new Leverhulme Postdoctoral Fellow. His research is in string theory, string phenomenology and quantum field theory.

Welcome, Federico

Explicit computation of injection and ejection impurity’s Green’s function reveals a generalisation of the Kubo-Martin-Schwinger relation.

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

DANGER

SciPost Physics accepts the paper “Finite temperature spin diffusion in the Hubbard model in the strong coupling limit” by Dr Oleksandr Gamayun et al.

Spin diffusion

Dr Andrei Stepanenko is our new Landau Junior Research Fellow. He works on topological photonics, combining topology and quantum computing.

Welcome, Andrei

The London Institute brings together experts from the worlds of finance and AI to discuss the potential and the pitfalls of AI-driven markets.

Converging futures

Three new closed-form expressions give the number of recursive divisors and ordered factorisations, which were until now hard to compute.

Counting recursive divisors

JHEP publishes the paper “Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces” co-authored by Prof. Yang-Hui He.

Bundled Laplacians

An analog of quasi-regular representations can be constructed for an infinite-dimensional group, despite the absence of the Haar measure.

Infinite-dimensional irreducibility

The recursive divisor function has a simple Dirichlet series that relates it to the divisor function and other standard arithmetic functions.

Recursive divisor properties

How gravitational waves are absorbed by a black hole is understood, for the first time, through effective on-shell scattering amplitudes.

Absorption with amplitudes

The beta function for a class of sigma models is found not to be geometric, but rather has an elegant form in the context of algebraic data.

Peculiar betas

A new open-source platform is specifically tailored for developing complex dialogue systems, like generative conversational AI assistants.

DeepPavlov dream

Number theorists gather at the London Institute to discuss cutting-edge research and present their latest work in this branch of mathematics.

Connected counting

The spin-spin correlation function of the Hubbard model reveals that finite temperature spin transport in one spatial dimension is diffusive.

Models trained on a Russian topical dataset, of knowledge-grounded human-human conversation, are capable of real-world tasks across languages.

Cross-lingual knowledge

A new way to estimate indices via representation theory reveals links to the sum-product phenomena and Zaremba’s conjecture in number theory.



Representation for sums

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

Speaking DNA

The UK premiere of Oliver Stone’s new film, Nuclear Now, takes place in the Lecture Theatre, followed by an interview with the director.

Nuclear Now

Genetic algorithms, which solve optimisation problems in a natural selection-inspired way, reveal previously unconstructed Calabi-Yau manifolds.

Genetic polytopes

Dr Oleksandr Gamayun is our latest Arnold Fellow. He works on applications of quantum field theory to problems in condensed matter theory.



Welcome, Oleksandr

Advances in Theoretical and Mathematics Physics accepts the paper “Mahler measuring the genetic code of amoebae” co-authored by Prof. Yang-Hui He.

Measuring amoebae

Approximating the basis of eigenfunctions allows for computational determination of the harmonic modes of bundle-valued Laplacians on Calabi-Yaus.

A piece in The Times explains how, thanks to our Arnold and Landau Fellowships, mathematicians divided by war find a common denominator.

The language of maths

The London Institute hosts a workshop on the Navier-Stokes millennium-prize problem and its connection to fluid computing and machine learning.

Towards fluid computing

For a finite set of integers with few prime factors, improving the lower bound on its sum and product sets affirms the Erdös-Szemerédi conjecture.

Sum-product with few primes

Prof. Oleksandr Kosyak joins us as our newest Arnold Fellow. His research focus is on representation theory of infinite-dimensional groups.

Finite Fields and Their Applications accepts the paper “On a girth–free variant of the Bourgain–Gamburd machine” by Prof. Ilya Shkredov.

Ungrouped machines

A complexity-science approach to digital twins of cities views them as interwoven self-organising phenomena, instead of machines or logistic systems.

Complex digital cities

We built a new navigation tool that makes it easier to search through all our papers, using filters such as subject, author and journal.

Research paper filters

The quadratic complexity of attention in transformers is tackled by combining token-based memory and segment-level recurrence, using RMT.

Upscaling memory

The journal Geometric and Functional Analysis publishes the paper “On the random Chowla conjecture” co-authored by Prof. Ilya Shkredov.

Random conjectures

At the Royal Institution's Friday Evening Discourse, Prof. Yang-Hui He recounts the creation of modern physics at the hands of geometry.

The geometry revolution

Our Trustee Martin Reeves explores imagination at its core, rethinking previous romantic notions, asking if we can harness it systematically.

Re-imagining imagination

Dr Mikhail Burtsev joins us as a Landau AI Fellow. His research focuses on mathematical tools and ideas that could lead to more intelligent AI.

Welcome, Mikhail

In The Spectator, our writer Madeleine Hall hails John Venn, who pioneered not only Venn diagrams but also frequentist probability.

What are the chances?

For each of our research papers, we show the papers most related to it by using a large language model to compute a distance function.

Semantic paper distance

In Sir Paul Nurse’s review of British science, he names the London Institute as one of five alternatives to the university model for research.

Nurse Review

A century ago, in our rooms in Mayfair, Sir James Dewar died. Our writer Thomas Hodgkinson pays tribute to the inventor of cordite in Nautilus.

The big bang

Prof. Ilya Shkredov discusses Zaremba’s elegant 1971 conjecture in the theory of continued fractions, and explores the bounds relating to it.

On Zaremba's conjecture

Research by Prof. Guido Caldarelli on the renormalisation group in complex networks features on the March 2023 cover of Nature Physics.

Nature cover

Prof. Alexander Esterov is our newest Arnold Fellow. He researches enumerative algebraic geometry, Galois theory and the geometry of polytopes.

Welcome, Alexander

Prof. Daniel Waldram introduces the formalism and tools for characterising geometries in gravitational theories, such as Calabi-Yau manifolds.

Geometry and fluxes

Insights from number theory suggest a new way to solve the critical Kauffman model, giving new bounds on the number and length of attractors.

Landau meets Kauffman

In the Russian press, we argue that our new Fellowships continue a venerable tradition of friendship between British and Russian scientists.

Science without borders

Мы в российской прессе о том, почему наши стипендии продолжают традицию дружбы между британскими и российскими учёными.

Наука без границ

Bursting cells can introduce noise in transcription factor screens, but modelling this process allows us to discern true counts from false.

Cell soup in screens

In a letter in The Times, our Director Thomas Fink argues that supporting independent research centres will accelerate discovery for Britain.

Accelerating science

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

Single-input Boolean networks

Designers and theorists talk about the intersection of design and mathematics in visualisation, architecture, digital design and industry.

Design meets maths

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