### Papers15 Sep

### Recursively divisible numbers

“Recursively divisible numbers” is accepted by the

*Journal of Number Theory*, which introduces a recursive analog of the divisor function.### People6 Sep

### Welcome, Evgeny

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

### press5 Sep

### Science goes pro

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

### PEOPLE21 Aug

### Welcome, Federico

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

### Papers15 Aug

### Mobile impurity

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

### Events24-25 AUG

### DANGER

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

### Papers3 Aug

### Spin diffusion

*SciPost Physics*accepts the paper “Finite temperature spin diffusion in the Hubbard model in the strong coupling limit”, by Dr Oleksandr Gamayun et al.### PEOPLE27 Jul

### Welcome, Andrei

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

### Events25 Jul

### Converging futures

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

### Papers25 Jul

### Counting recursive divisors

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

### Papers21 Jul

### Bundled Laplacians

*JHEP*publishes the paper “Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces”, co-authored by Prof. Yang-Hui He.### Papers20 Jul

### Infinite-dimensional irreducibility

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

### Papers17 Jul

### Recursive divisor properties

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

### Papers14 Jul

### Absorption with amplitudes

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

### Papers13 Jul

### Peculiar betas

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.

### Papers12 Jul

### DeepPavlov dream

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

### Events3 Jul

### Connected counting

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

### Papers23 Jun

### Spin diffusion

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

### Papers21 Jun

### Cross-lingual knowledge

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

### Papers20 Jun

### Representation for sums

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

### Papers16 Jun

### Speaking DNA

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

### Events14 Jun

### Nuclear Now

The UK premiere of Oliver Stone’s new film,

*Nuclear Now*, takes place in the Lecture Theatre, followed by an interview with the director.### Papers13 Jun

### Genetic polytopes

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

### Papers2 Jun

### Exponential Kauffman scaling

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

### people26 May

### Welcome, Oleksandr

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

### Papers25 May

### Measuring amoebae

*Advances in Theoretical and Mathematics Physics*accepts the paper “Mahler measuring the genetic code of amoebae”, co-authored by Prof. Yang-Hui He.### Papers24 May

### Bundled Laplacians

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

### Press22 May

### The language of maths

A piece in

*The Times*explains how, thanks to our Arnold and Landau Fellowships, mathematicians divided by war find a common denominator.### Events16 May

### Towards fluid computing

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

### Papers12 May

### Sum-product with few primes

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.

### people9 May

### Welcome, Oleksandr

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

### Papers2 May

### Ungrouped machines

*Finite Fields and Their Applications*accepts the paper “On a girth–free variant of the Bourgain–Gamburd machine,” by Prof. Ilya Shkredov.### Papers1 May

### Complex digital cities

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

### Website28 Apr

### Research paper filters

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

### Papers24 Apr

### Upscaling memory

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

### website19 Apr

### Funding news

We created a new page on our website that gives a human perspective on our different sources of funding, and what each gift is used for.

### Papers18 Apr

### Random conjectures

The journal

*Geometric and Functional Analysis*publishes the paper “On the random Chowla conjecture”, co-authored by Prof. Ilya Shkredov.### Events12 Apr

### The geometry revolution

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

### Events10 Apr

### Re-imagining imagination

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

### people5 Apr

### Welcome, Mikhail

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.

### News4 Apr

### What are the chances?

In

*The Spectator*, our writer Madeleine Hall hails John Venn, who pioneered not only Venn diagrams but also frequentist probability.### Website31 Mar

### Semantic paper distance

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.

### News22 Mar

### Nurse Review

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.

### News21 Mar

### The big bang

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*.### Events17 Mar

### On Zaremba's conjecture

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

### News17 Mar

### Nature cover

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

*Nature Physics*.### people14 Mar

### Welcome, Alexander

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

### Events7 Mar

### Geometry and fluxes

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

### Papers3 Mar

### Landau meets Kauffman

A new, simple approach to the critical Kauffman model with connectivity one sharpens the bounds on the number and length of attractors.

### perspectives21 Feb

### Science without borders

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

### Press21 Feb

### Наука без границ

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

### Papers16 Feb

### Cell soup in screens

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

### Press13 Feb

### Accelerating science

In a letter in

*The Times*, our Director Thomas Fink argues that supporting independent research centres will accelerate discovery for Britain.### Papers13 Feb

### Single-input Boolean networks

A new, simpler approach to the critical Kauffman model with connectivity one reveals that it has more attractors than previously believed.

### Events31 Jan

### Design meets maths

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

### Events30 Jan

### Conformal bootstrap

Dr Andreas Stergiou delivers an introduction to the conformal bootstrap method which is used to constrain and solve conformal field theories.

### News26 Jan

### Conway Prize

The London Institute is establishing an annual prize of £500 for the best short paper in theoretical research written by one of its members.

### Papers22 Jan

### Multiplicativity of sets

Expanding the known multiplicative properties of large difference sets yields a new, quantitative proof on the structure of product sets.

### design18 Jan

### Writing rules guide

Part of our design guide, our writing style guide is a collection of rules for writing and typesetting our website and research papers.

### Papers30 Dec 2022

### Bounding Zaremba’s conjecture

Using methods related to the Bourgain–Gamburd machine refines the previous bound on Zaremba’s conjecture in the theory of continued fractions.