Our goal is to boost our research output for 2024 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 40 points for this year.

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  • Gravitational observables from scattering amplitudes (Review paper)

    AOA. OchirovJVM 2.91 Concept for Physics Reports

    Scattering amplitude dynamics

    We review classical gravitational dynamics derived from quantum field theoretic scattering amplitudes, a tool used in detecting gravitational waves.

  • The combinatorics of the Morse discriminant

    AEA. EsterovAV 1 Concept for Journal of Combinatorial Theory. Series B

    Morse discriminant combinatorics

    The rich combinatorics of the recently-computed Newton polytope of the Morse discriminant provides insights on connections between algebra, geometry and combinatorics.

  • Multiple solutions of enumerative problems


    AEA. EsterovDM 0.51 Concept for Arnold Mathematical Journal

    Multiple solutions of enumerative

    In enumerative geometry, when constraints, such as lines, are in special positions, several solutions of a problem collide to form a multiple solution.

  • Topological protection of quantum state structure

    Topological photonics

    ASA. StepanenkoLSMG 0.31 Concept for Physical Review A

    Topological protection

    Ideas from topology are used to show the protection of quantum state density matrix elements, revealing new applications of topological photonics.

  • 0.21 Concept for Journal of High Energy Physics

    Gravitational interactions of massiv

    Formulating, for the first time, field theories for massive higher-spin particles for the potential application to black-hole dynamics.


  • Immortality unleashed

    TFT. FinkYHY. He 2.29 Draft for Physical Review Letters

    Immortality unleashed

    Ageing does not confer a benefit toward natural selection in a changing environment.

  • Establishing irreducibility of representations via Gram determinants

    AVA. V. Kosyak 1.77 Draft for Journal of Functional Analysis

    Irreducibility via Gram determinants

    A combination of techniques proves the irreducibility of unitary representations of infinite-dimensional groups based on Gram determinants.

  • TFT. FinkFSF. Sheldon 1.24 Draft for Discrete Mathematics

    Kauffman math


  • Properties of the recursive divisor function

    Number theory

    TFT. Fink 1.05 Draft for Proceedings of the American Mathematical Society

    Recursive divisor properties

    The recursive divisor function is found to have a simple generating function, which leads to a number of new Dirichlet convolutions.

  • 1.02 Draft for Proceedings of the National Academy of Sciences of the USA

    Learning Gibbs measures

    Even when the dynamics of a glass combine into a single metastable state, we can still learn the couplings accurately.

  • 0.97 Draft for Physical Review E

    Fractal columns


  • 0.86 Draft for Annali della Scuola normale superiore di Pisa - Classe di scienze

    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.

  • Condensed matter theory

    0.78 Draft for Nature Physics

    Odd topological kinks

    Topological kinks in matter with non-reciprocal bonds that do not conserve energy can be studied through experiment, simulations and theory.

  • 0.61 Draft for Proceedings of the National Academy of Sciences of the USA

    Murmurations of L-functions

    Investigating oscillating patterns for Dirichelt coefficients of low-degree arithmetic L-functions gives insight into this newly-discovered phenomena.

  • Chiral photon states

    0.55 Draft for Physical Review Research

    Bound states with π flux

    The interplay between the interactions and chirality of bound photons reveals insight into, and can even predict new physics.

  • 0.45 Draft for Bioinformatics

    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.

  • 0.37 Draft for Journal of Combinatorial Algebra

    Morse discriminant combinatorics


  • Algebraic geometry

    0.37 Draft for Journal of Combinatorial Algebra

    Topology of tropical polynomials

    Tropical geometric objects share many characteristics with classical algebraic geometry objects. We study this correspondence for the topology of polynomials.

  • 0.34 Draft for Communications in Mathematical Physics

    MSSM vacuum structure

    On the vacuum structure of the minimal supersymmetric standard model, which considers only particle states and interactions consistent with reality.

  • 0.33 Draft for Physical Review B

    Quantum transport

    Quantum geometric tensor exploration to solve a variational problem of state transport in quantum nets.

  • Algebraic geometry

    0.3 Draft for Physics Letters B


    Pachner graphs for 3-manifold triangulation can be generated and analysed through the lens of network science.

  • Draft

    Combinatoric Topological Strings

    We find a physical interpretation, in terms of combinatorial topological string theory, of a classic result in finite group theory theory.


  • The mathematical structure of innovation

    Theory of innovation

    TFT. FinkITI. Teimouri 3.04 Arxiv for Science Advances

    Recursive structure of innovation

    A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

  • Some new results on the higher energies I

    Number theory

    ISI. Shkredov 2.43 Arxiv for Geometric and Functional Analysis

    Higher 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.

  • AEA. Esterov 2.07 Arxiv for Proceedings of the London Mathematical Society

    Engineered complete intersections


  • Recursively abundant and recursively perfect numbers

    Number theory

    TFT. Fink 1.71 Arxiv for Journal of 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

    1.42 Arxiv for Nature

    Speaking DNA

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

  • Algebraic geometry

    1.22 Arxiv for American Journal of Mathematics

    Symmetric spatial curves

    The geometry of symmetric spatial curves reveals characterisations of general one-parameter families of complex univariate polynomials with fully-symmetric Galois groups.

  • Number theory

    1.05 Arxiv for Proceedings of the American Mathematical Society

    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

    0.99 Arxiv for Journal of Physics A

    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.

  • Computational linguistics

    0.5 Arxiv for AINL 2023

    Cross-lingual knowledge

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

  • 0.42 Arxiv for Arkiv for Mathematik

    Slight degeneration

    Newton polytopes are used to study systems of general polynomial equations, which consist of given monomials with generic coefficients. We describe what happens to solutions of these systems when the coefficients slightly degenerate.

  • 0.21 Arxiv for Journal of High Energy Physics

    Gauge interactions

    Formulating, for the first time, field theories for massive higher-spin particles for the potential application to black-hole dynamics.

  • 0.17 Arxiv for International Journal of Data Science in the Mathematical Sciences

    Machine learning polytopes

    A supervised machine of learning lattice polytopes predicts properties of volume, dual volume, and reflexivity with up to 100% accuracy.

Submitted home

  • Characterizing contaminant noise in barcoded perturbation experiments

    Synthetic biology

    FSF. Sheldon 3.06 Sub. to Proceedings of the National Academy of Sciences of the USA

    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.

  • Biological logics are restricted


    TFT. FinkRHR. Hannam 2.65 Sub. to National Science Review

    In 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.

  • Mortality equation offers a theory for programmed aging


    TFT. Fink 2.12 Sub. to Nature Ageing

    I 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 of ordered factorizations and recursive divisors

    Number theory

    TFT. Fink 1.04 Sub. to Journal of Number Theory

    Counting 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

    0.89 Sub. to Journal of Functional Analysis

    Infinite dimensional irreducibility

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

Submitted away

  • The height of an infinite parallelotope is infinite

    Representation theory

    AVA. V. Kosyak 1.77 Sub. to Journal of Functional Analysis

    Infinitely high parallelotopes

    The height of an infinite parallelotope is infinite, an essential ingredient to prove the irreducibility of unitary representations of some infinite-dimensional groups.

  • Some applications of representation theory to the sum–product phenomenon


    ISI. Shkredov 1.53 Sub. to Journal of Algebraic Combinatorics

    Representation 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.

  • On Korobov bound concerning  Zaremba's conjecture

    Number theory

    NMBMISI. Shkredov 1.52 Sub. to Journal of the American Mathematical Society

    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.

  • On the distribution of quadratic residues


    ISI. Shkredov 1.3 Sub. to Finite Fields and Their Applications

    Quadratic 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.

  • Machine learning

    1.17 Sub. to Conference on Neural Information Processing Systems

    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 physics

    0.99 Sub. to Journal of Physics A

    Landau meets Kauffman

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

  • 0.82 Sub. to Neural Computation

    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.

  • Number theory

    0.67 Sub. to Duke Mathematical Journal

    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.

  • 0.66 Sub. to Algebraic Geometry

    Sparse curve singularities


  • Number theory

    0.57 Sub. to Communications in Mathematical Physics

    Reflexions on Mahler

    With physically-motivated Newton polynomials from reflexive polygons, we find the Mahler measure and dessin d’enfants are in 1-to-1 correspondence.

  • Number theory

    0.39 Sub. to Journal of Symbolic Computation

    Elliptic curve murmurations

    Certain properties of the bivariate cubic equations used to prove Fermat’s last theorem exhibit flocking patterns, machine learning reveals.

  • 0.26 Sub. to ACL Rolling Review

    From words to blocks

    Combining a language model with reinforcement learning enables object construction in a Minecraft-like environment from natural language instructions.


  • Non-reciprocal topological solitons in active metamaterials

    Condensed matter theory

    JVOGO. GamayunXGASCM... 1.89 In press Nature

    Strange kinks

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

  • Permuting the roots of univariate polynomials whose coefficients depend on parameters

    AEA. EsterovLL 1.27 Acc. to Journal of the European Mathematical Society

    Permuting the roots

    We combine topology of braids and tropical geometry to describe the Galois group of a typical rational function composed of prescribed monomials. The same new technique solves several similar multivariate problems.

  • Exact dynamics of the critical Kauffman model with connectivity one

    Statistical physics

    TFT. Fink 1.09 Acc. to Physical Review Research

    Multiplicative loops

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

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

    Condensed matter theory

    OGO. GamayunEQKBMB 0.23 Physical Review A

    Spin-charge separation

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