Our goal is to boost our research output for 2025 by √2 over our previous year. We measure our research output by SNIP points, which are described in our Journals page. Help us reach our target of 56 points for this year.
Drafts
TF
YH
2.29 Draft for Physical Review LettersImmortality unleashed
Ageing does not confer a benefit toward natural selection in a changing environment.
AV
1.77 Draft for Journal of Functional AnalysisIrreducibility via Gram determinants
A combination of techniques proves the irreducibility of unitary representations of infinite-dimensional groups based on Gram determinants.
TF
FS
1.24 Draft for Discrete MathematicsDirichlet meets Kauffman
Long the province of statistical physics, the structure of the Kauffman model of genetic computation is uncovered via Dirichlet convolutions.
Number theory
Recursive divisor properties
The recursive divisor function is found to have a simple generating function, which leads to a number of new Dirichlet convolutions.
Learning Gibbs measures
Even when the dynamics of a glass combine into a single metastable state, we can still learn the couplings accurately.
Singularities of discriminants
Investigating to what extent Whitney's theorem holds true for more general universal polynomials such as A-discriminants by Gelfand, Kapranov and Zelevinsky.
Design and interpretation of transcr
Graph models representing the steps in transcription factor screens reveal the most costly error sources and most promising set of factors.
Algebraic geometry
Topology of tropical polynomials
Tropical geometric objects share many characteristics with classical algebraic geometry objects. We study this correspondence for the topology of polynomials.
MSSM vacuum structure
On the vacuum structure of the minimal supersymmetric standard model, which considers only particle states and interactions consistent with reality.
Statistics
Paying for science
An analysis of UKRI grant funding gives a strategy for maximising unrestricted funds, thereby helping research centres cover their costs.
Arxiv
Theory of innovation
TF
IT
3.04 Arxiv for Science AdvancesRecursive structure of innovation
A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.
Number theory
IS
2.43 Arxiv for Geometric and Functional AnalysisHigher energies
Generalising the recent Kelley–Meka result on sets avoiding arithmetic progressions of length three leads to developments in the theory of the higher energies.
Algebraic geometry
AE
2 Arxiv for Journal of Combinatorial Theory. Series BSlight degenerations
The tools used to study polynomial equations with indeterminate coefficients are extended to some important cases with interrelated ones.
Algebraic geometry
AE
1.83 Arxiv for Advances in MathematicsSchön complete intersections
A uniform approach to a class of varieties is described that includes important types of objects from geometry, optimisation and physics.
Number theory
Ample and pristine numbers
Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.
Machine learning
Speaking DNA
A family of transformer-based DNA language models can interpret genomic sequences, opening new possibilities for complex biological research.
Algebraic geometry
Symmetric spatial curves
We study the geometry of generic spatial curves with a symmetry in order to understand the Galois group of a family of sparse polynomials.
Number theory
Recursive divisor properties
The recursive divisor function has a simple Dirichlet series that relates it to the divisor function and other standard arithmetic functions.
Evolvability
Flowers of immortality
The eigenvalues of the mortality equation fall into two classes—the flower and the stem—but only the stem eigenvalues control the dynamics.
Condensed matter theory
Counting free fermions
We link the statistical properties of one-dimensional systems of free fermions initialised in states of either half- or alternating-occupancy.
Computational linguistics
Cross-lingual knowledge
Models trained on a Russian topical dataset, of knowledge-grounded human-human conversation, are capable of real-world tasks across languages.
Condensed matter theory
Non-reciprocal breather
Producing the first examples of breathing solitons in one-dimensional non-reciprocal media allows their propagation dynamics to be analysed.
Machine learning polytopes
A supervised machine of learning lattice polytopes predicts properties of volume, dual volume, and reflexivity with up to 100% accuracy.
Algebraic geometry
Linearising actions
We give a solution of the linearisation problem in the Cremona group of rank two over an algebraically closed field of characteristic zero.
High energy physics
A New leptogenesis
We propose that dark matter consists of topological order, so gapped anyon excitations decay to generate the Standard Model's lepton asymmetry.
Submitted home
Synthetic biology
FS
3.06 Sub. to Proceedings of the National Academy of Sciences of the USACell soup in screens
Bursting cells can introduce noise in transcription factor screens, but modelling this process allows us to discern true counts from false.
Evolvability
TF
2.12 Sub. to Nature AgeingI want to be forever young
The mortality equation governs the dynamics of an evolving population with a given maximum age, offering a theory for programmed ageing.
Number theory
TF
1.04 Sub. to Journal of Number TheoryCounting recursive divisors
Three new closed-form expressions give the number of recursive divisors and ordered factorisations, which were until now hard to compute.
Representation theory
AV
PM 0.89 Sub. to Journal of Functional AnalysisInfinite dimensional irreducibility
The criteria of irreducibility of representations of the inductive limit of certain general linear groups acting on three infinite rows.
Submitted away
Combinatorics
TF
RH
2.65 Sub. to National Science ReviewIn life, there are few rules
The bipartite nature of regulatory networks means gene-gene logics are composed, which severely restricts which ones can show up in life.
Combinatorics
TF
2.44 Sub. to Proceedings of the National Academy of Sciences of the USAStructure of genetic computation
The structural and functional building blocks of gene regulatory networks correspond, which tell us how genetic computation is organised.
Combinatorics
TF
2.44 Sub. to Proceedings of the National Academy of Sciences of the USABiological logics are restricted
The fraction of logics that are biologically permitted can be bounded and shown to be tiny, which makes inferring them from experiments easier.
Combinatorics
IS
1.53 Sub. to Journal of Algebraic CombinatoricsRepresentation for sum-product
A new way to estimate indices via representation theory reveals links to the sum-product phenomena and Zaremba’s conjecture in number theory.
Number theory
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.
Algebraic geometry
Permuting the roots
The Galois group of a typical rational function is described and similar problems solved using the topology of braids and tropical geometry.
Quantum field theory
Continuous quivers
Continuous quivers enable exact Wilson loop calculation, reveal an emergent dimension, and raise tantalising questions on dual strings.
Machine learning
BERT enhanced with recurrence
The quadratic complexity of attention in transformers is tackled by combining token-based memory and segment-level recurrence, using RMT.
Statistical mechanics
Fredholm meets Toeplitz
A new approach to the large distance asymptotic of the finite-temperature deformation is discussed for a sine-kernel Fredholm determinant.
Free energy and learning
Using the free energy principle to derive multiple theories of associative learning allows us to combine them into a single, unifying framework.
Representation theory
Group representation irreducibility
A general approach to proving the irreducibility of representations of infinite-dimensional groups within the frame of Ismagilov's conjecture.
Number theory
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.
Algebraic geometry
Sparse singularities
Geometric properties, including delta invariants, are computed for singular points defined by polynomials with indeterminate coefficients.
AI-assisted maths
Metaheuristic tilings
We use simulated annealing to efficiently construct all brane tilings that encode supersymmetric gauge theories and discover a new one.
AI-assisted maths
Learning to be Simple
Neural networks classify simple finite groups by generators, unlike earlier methods using Cayley tables, leading to a proven explicit criterion.
String theory
Futaki for reflexives
We compute Futaki invariants for gauge theories from D3-branes that probe toric Calabi-Yau singularities arising from reflexive polytopes.
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From words to blocks
Combining a language model with reinforcement learning enables object construction in a Minecraft-like environment from natural language instructions.
Algebraic geometry
Three-manifolds
Pachner graphs for 3-manifold triangulation can be generated and analysed through the lens of network science.
AI-assisted maths
Convolution in topology
Using Inception, a convolutional neural network, we predict certain divisibility invariants of Calabi-Yau manifolds with up to 90% accuracy.
Published
Linear algebra
AV
1.42 Linear Algebra and its ApplicationsInfinite parallelotope
We study the geometry of finite dimensional space as the dimension grows to infinity with an accent on the height of the parallelotope.
Combinatorics
IS
1.3 In press Finite Fields and Their ApplicationsQuadratic residues
Additive combinatorics sheds light on the distribution of the set of squares in the prime field, revealing a new upper bound for the number of gaps.
Representation theory
AV
PM 0.26 In press Journal of Lie TheoryIrreducible group action
We construct the unitary representation of an infinite-dimensional general linear group acting on a space and establish its irreducibility.