“Recursively divisible numbers” is accepted by the Journal of Number Theory, which introduces a recursive analog of the divisor function.
Dr Evgeny Sobko is our new Landau Fellow. His research focuses on exactly solvable models in quantum field and string theory.
Professional sport has a lot to teach scientists about pushing the limits of human achievement—so why are we still content to be amateurs?
Dr Federico Carta is our new Leverhulme Postdoctoral Fellow. His research is in string theory, string phenomenology and quantum field theory.
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.
SciPost Physics accepts the paper “Finite temperature spin diffusion in the Hubbard model in the strong coupling limit”, by Dr Oleksandr Gamayun et al.
Dr Andrei Stepanenko is our new Landau Junior Research Fellow. He works on topological photonics, combining topology and quantum computing.
The London Institute brings together experts from the worlds of finance and AI to discuss the potential and the pitfalls of AI-driven markets.
Three new closed-form expressions give the number of recursive divisors and ordered factorisations, which were until now hard to compute.
JHEP publishes the paper “Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces”, co-authored by Prof. Yang-Hui He.
An analog of quasi-regular representations can be constructed for an infinite-dimensional group, despite the absence of the Haar measure.
The recursive divisor function has a simple Dirichlet series that relates it to the divisor function and other standard arithmetic functions.
How gravitational waves are absorbed by a black hole is understood, for the first time, through effective on-shell scattering 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.
A new open-source platform is specifically tailored for developing complex dialogue systems, like generative conversational AI assistants.
Number theorists gather at the London Institute to discuss cutting-edge research and present their latest work in this branch of mathematics.
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.
A new way to estimate indices via representation theory reveals links to the sum-product phenomena and Zaremba’s conjecture in number theory.
A family of transformer-based DNA language models can interpret genomic sequences, opening new possibilities for complex biological research.
The UK premiere of Oliver Stone’s new film, Nuclear Now, takes place in the Lecture Theatre, followed by an interview with the director.
Genetic algorithms, which solve optimisation problems in a natural selection-inspired way, reveal previously unconstructed Calabi-Yau manifolds.
Surprisingly, the number of attractors in the critical Kauffman model with connectivity one grows exponentially with the size of the network.
Dr Oleksandr Gamayun is our latest Arnold Fellow. He works on applications of quantum field theory to problems in condensed matter theory.
Advances in Theoretical and Mathematics Physics accepts the paper “Mahler measuring the genetic code of amoebae”, co-authored by Prof. Yang-Hui He.
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 London Institute hosts a workshop on the Navier-Stokes millennium-prize problem and its connection to fluid computing and machine learning.
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.
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.
A complexity-science approach to digital twins of cities views them as interwoven self-organising phenomena, instead of machines or logistic systems.
We built a new navigation tool that makes it easier to search through all our papers, using filters such as subject, author and journal.
The quadratic complexity of attention in transformers is tackled by combining token-based memory and segment-level recurrence, using RMT.
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.
The journal Geometric and Functional Analysis publishes the paper “On the random Chowla conjecture”, co-authored by Prof. Ilya Shkredov.
At the Royal Institution's Friday Evening Discourse, Prof. Yang-Hui He recounts the creation of modern physics at the hands of geometry.
Our Trustee Martin Reeves explores imagination at its core, rethinking previous romantic notions, asking if we can harness it systematically.
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.
In The Spectator, our writer Madeleine Hall hails John Venn, who pioneered not only Venn diagrams but also frequentist probability.
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.
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.
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.
Prof. Ilya Shkredov discusses Zaremba’s elegant 1971 conjecture in the theory of continued fractions, and explores the bounds relating to it.
Research by Prof. Guido Caldarelli on the renormalisation group in complex networks features on the March 2023 cover of Nature Physics.
Prof. Alexander Esterov is our newest Arnold Fellow. He researches enumerative algebraic geometry, Galois theory and the geometry of polytopes.
Prof. Daniel Waldram introduces the formalism and tools for characterising geometries in gravitational theories, such as Calabi-Yau manifolds.
A new, simple approach to the critical Kauffman model with connectivity one sharpens the bounds on the number and length of attractors.
In the Russian press, we argue that our new Fellowships continue a venerable tradition of friendship between British and Russian scientists.
Мы в российской прессе о том, почему наши стипендии продолжают традицию дружбы между британскими и российскими учёными.
Bursting cells can introduce noise in transcription factor screens, but modelling this process allows us to discern true counts from false.
In a letter in The Times, our Director Thomas Fink argues that supporting independent research centres will accelerate discovery for Britain.
A new, simpler approach to the critical Kauffman model with connectivity one reveals that it has more attractors than previously believed.
Designers and theorists talk about the intersection of design and mathematics in visualisation, architecture, digital design and industry.
Dr Andreas Stergiou delivers an introduction to the conformal bootstrap method which is used to constrain and solve conformal field theories.
The London Institute is establishing an annual prize of £500 for the best short paper in theoretical research written by one of its members.
Expanding the known multiplicative properties of large difference sets yields a new, quantitative proof on the structure of product sets.
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
Using methods related to the Bourgain–Gamburd machine refines the previous bound on Zaremba’s conjecture in the theory of continued fractions.