O. Gamayun

A. Losev

M. Shifman

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

First-order formalism for β functions in bosonic sigma models from supersymmetry breaking

Peculiar betas tamed

A. Esterov

A uniform approach to a class of varieties is described that includes important types of objects from geometry, optimisation and physics.

Schön complete intersections

The tools used to study polynomial equations with indeterminate coefficients are extended to some important cases with interrelated ones.

Engineered complete intersections: slightly degenerate Bernstein-Kouchnirenko-Khovanskii

Slight degenerations

M. Brandenbourger

J. Veenstra

F. Gorp

H. Terwisscha-Dekker

J. Caux

C. Coulais

Producing the first examples of breathing solitons in one-dimensional non-reciprocal media allows their propagation dynamics to be analysed.

Non-reciprocal breathing solitons

Non-reciprocal breather

Y. He

Reviewing progress in the field of AI-assisted discovery for maths and theoretical physics reveals a triumvirate of different approaches.

AI-driven research in pure mathematics and theoretical physics

On AI-driven discovery

P. Berglund

G. Butbaia

E. Heyes

E. Hirst

V. Jejjala

Machine learning generates desirable triangulations of geometric objects that are required for Calabi-Yau compactification in string theory.

Generating triangulations and fibrations with reinforcement learning

Triangulating polytopes

A. Renner

F. Sheldon

A. Zlotnik

L. Tao

A. Sornborger

The training algorithm for digital neural networks is adapted and implemented entirely on an experimental chip inspired by brain physiology.

The backpropagation algorithm implemented on spiking neuromorphic hardware

Spiky backpropagation

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

Full-counting statistics for the alternating and domain-wall states

Counting free fermions

A. V. Kosyak

A general approach to proving the irreducibility of representations of infinite-dimensional groups within the frame of Ismagilov's conjecture.

The generalized characteristic polynomial, corresponding resolvent and their application

Group representation irreducibility

O. Lychkovskiy

Modelling the final state of a mobile impurity particle immersed in a one-dimensional quantum fluid after the abrupt application of a force.

One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results

A kicked polaron

L. Cangemi

M. Chiodaroli

H. Johansson

A. Ochirov

P. Pichini

E. Skvortsov

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

Compton Amplitude for Rotating Black Hole from QFT

QFT illuminates black holes

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

From higher-spin gauge interactions to Compton amplitudes for root-Kerr

Root-Kerr from higher-spin theory

V. Kazakov

E. Sobko

K. Zarembo

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

Large-N principal chiral model in arbitrary external fields

PCM in arbitrary fields

E. Statnik

A. Voorhaar

Geometric properties, including delta invariants, are computed for singular points defined by polynomials with indeterminate coefficients.

Sparse curve singularities, singular loci of resultants, and Vandermonde matrices

Sparse singularities

L. Lang

The Galois group of a typical rational function is described and similar problems solved using the topology of braids and tropical geometry.

Permuting the roots of univariate polynomials whose coefficients depend on parameters

Permuting the roots

S. Chen

P. Dechant

D. Riabchenko

Coxeter transformations for root diagrams of simply-laced Lie groups are exhaustively computed then machine learned to very high accuracy.

Machine Learning Clifford invariants of ADE Coxeter elements

Clifford invariants by ML

X. Guo

A. Sarvi

C. Meinersen

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

Non-reciprocal topological solitons in active metamaterials

Strange kinks

M. Burtsev

M. Reeves

A. Job

Large language models like ChatGPT can generate human-like text but businesses that overestimate their abilities risk misusing the technology.

The working limitations of large language models

The limits of LLMs

I. Shkredov

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

On some multiplicative properties of large difference sets

Multiplicativity of sets

We demonstrate that the height of an infinite parallelotope is infinite if no non-trivial combinations of its edges belong to $l_2(\mathbb N)$.

We demonstrate that the height of an infinite parallelotope is infinite if no non-trivial combinations of its edges belong to <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi mathvariant="double-struck">N</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">l_2(\mathbb N)</annotation></semantics></math>l2​(N).

The height of an infinite parallelotope is infinite

Infinitely high parallelotopes

V. F. Lev

A cyclic group with small difference set has a nonzero element for which the second largest number of representations is twice the average.

The popularity gap

M. Panfil

F. Taha Sant'Ana

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

Kubo-Martin-Schwinger relation for an interacting mobile impurity

Mobile impurity

Investigating cluster algebras through the lens of modern data science reveals an elegant symmetry in the quiver exchange graph embedding.

Cluster algebras: network science and machine learning

AI for cluster algebras

T. Fink

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

Number of ordered factorizations and recursive divisors

Counting recursive divisors

A. Ashmore

B. A. Ovrut

By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.


Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces

Bundled Laplacians

P. Moree

The criteria of irreducibility of representations of the inductive limit of certain general linear groups acting on three infinite rows.

Irreducibility of the Koopman representations for the group GL0(2∞,R), acting on three infinite rows

Infinite dimensional irreducibility

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

Properties of the recursive divisor function and the number of ordered factorisations

Recursive divisor properties

R. Aoude

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

Gravitational partial-wave absorption from scattering amplitudes

Absorption with amplitudes

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

Peculiarities of beta functions in sigma models

Peculiar betas

D. Zharikova

D. Kornev

F. Ignatov

M. Talimanchuk

D. Evseev

K. Petukhova

V. Smilga

D. Karpov

Y. Shishkina

D. Kosenko

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

DeepPavlov dream: platform for building generative AI assistants

DeepPavlov dream

D. Aggarwal

H. N. Sá Earp

T. Silva

Topological quantities for the Calabi-Yau link construction of G2 manifolds are computed and machine learnt with high performance scores.


Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds

Computing Sasakians

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

Monolingual and cross-lingual knowledge transfer for topic classification

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.

Some applications of representation theory to the sum–product phenomenon

Representation for sum-product

V. Fishman

Y. Kuratov

M. Petrov

A. Shmelev

D. Shepelin

N. Chekanov

O. Kardymon

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


GENA-LM: A family of open-source foundational models for long DNA sequences

Speaking DNA

A. Lukas

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

New Calabi-Yau manifolds from genetic algorithms

Genetic polytopes

A. Hutsalyuk

B. Pozsgay

M. B. Zvonarev

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

Finite temperature spin diffusion in the Hubbard model in the strong coupling limit

Spin diffusion

E. Quinn

K. Bidzhiev

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

Emergence of anyonic correlations from spin and charge dynamics in one dimension

Spin-charge separation

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

Number of attractors in the critical Kauffman model is exponential

Kauffman cracked

A. Nestor

A. Zahabi

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

Mahler measuring the genetic code of amoebae

Analysing amoebae

A new connection between continued fractions and the Bourgain–Gamburd machine reveals a girth-free variant of this widely-celebrated theorem.

On a girth-free variant of the Bourgain–Gamburd machine

Ungrouped machines

G. Caldarelli

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


Eigenvalues of neutral networks

Eigenvalues of neutral networks: interpolating between hypercubes