Articles

Ordered by date of initial arXiv upload, not by date of final publication.

Geometry and Topology

  1. Simplicial presheaves of Green complexes and twisting cochains
    Timothy Hosgood, Mahmoud Zeinalian
    Higher Structures 10 2026 292–368
    10.21136/HS.2026.09
    2308.09627 [math.AG]
  2. Various notions of (co)simplicial (pre)sheaves
    Communications in Mathematics 32 2024
    10.46298/cm.10359
    2205.15185 [math.CT]
  3. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
    manuscripta mathematica 173 2023 925–960
    10.1007/s00229-023-01484-5
    2003.10591 [math.AG]
  4. Simplicial Chern-Weil theory for coherent analytic sheaves, part I
    Bulletin de la Société Mathématique de France 151 2023 127–170
    10.24033/bsmf.2866
    2003.10023 [math.AG]

(Applied) Category Theory

  1. Psymple: A Python package for complex systems modelling
    George Simmons, David Stern, Georg Osang, Luigi Ponti, Andrew Paul Gutierrez, Chiara Facciolà, Timothy Hosgood
    The Journal of Open Source Software 10 2025
    10.21105/joss.07364
  2. The diagrammatic presentation of equations in categories
    Kevin Arlin, James Fairbanks, Tim Hosgood, Evan Patterson
    unpublished 2024
    2401.09751 [math.CT]
  3. A diagrammatic view of differential equations in physics
    Evan Patterson, Andrew Baas, Timothy Hosgood, James Fairbanks
    Mathematics in Engineering 5 2022
    10.3934/mine.2023036
    2204.01843 [math-ph]
  4. Deep neural networks as nested dynamical systems
    David I Spivak, Timothy Hosgood
    Published on SIAM News Blog (2021-12-01), available here
    2111.01297 [cs.LG]
  5. Dirichlet polynomials and entropy
    David I Spivak, Timothy Hosgood
    Entropy 23 2021
    10.3390/e23081085
    2107.04832 [cs.IT]

Books

  1. An introduction to quantum information science
    qubit.guide
    Joint work with Artur Ekert, Alastair Kay, and Chiara Macchiavello: an open-source introductory textbook on the fundamentals of theoretical quantum computing

Theses

  1. Chern classes of coherent analytic sheaves: a simplicial approach
    tel-02882140
    2020 PhD thesis; supervised by Julien Grivaux and Damien Calaque
  2. Under Spec Z: a reader's companion
    [PDF]
    2016 Primary master's thesis; supervised by Kobi Kremnitzer and Christopher Hollings
  3. Death and extended persistence in computational algebraic topology
    1609.00920 [math.AT]
    2016 Secondary master's thesis; unsupervised
  4. An introduction to varieties in weighted projective space
    1604.02441 [math.AG]
    2016 Undergraduate project supervised by Balázs Szendrői; sincere caveat lector

Videos and slides

    2026

  1. The responsibilities of decontextualisers
    Keynote talk: Diversity and Decolonisation in Mathematics and its Applications (Warwick University)
    [Slides: HTML]
    An extended reading list, with some thoughts and selected quotes, on how decolonisation can help us to face our responsibilities as mathematicians, "stewards of abstraction".
  2. Why Build a Categorical Model?
    Oxford Seminar (Topos Institute)
    [Slides: HTML]
    What do we gain from building an ODE model "categorically", and how can software help such a process? Based on two blog posts: Part 1 and Part 2

    3. 2025

  3. Abstractions for real people
    Invited talk (New Paltz SUNY)
    [Slides: PDF]
    When do abstractions in mathematics, computer science, and technology support people? What might it mean to do mathematics "for public benefit"? Jointly written with Brendan Fong
  4. Čech data for holomorphic Chern classes
    Geometry, Topology, and Physics Seminar (New York University Abu Dhabi)
    [Slides: PDF]
    Some explicit calculations of Atiyah classes as elements in the total complex of the Čech-de Rham bicomplex, as carried out in my PhD thesis
  5. Open translations in mathematics
    Modern History of Mathematics, Isaac Newton Institute
    [Slides: PDF] [Abstract] [Video: YouTube]
    An overview of some difficulties in historical mathematical translation, and discussion of possible future community projects

    6. 2024

  6. Loose simplicial objects
    New York City Category Theory Seminar
    [Slides: PDF]
    An introduction to the sorts of coherence conditions that appear when calculating certain homotopy limits in geometry

    7. 2022

  7. Diagrammatic differential equations
    Applied Category Theory 2022
    [Slides: PDF] [Video: YouTube]
    Overview of the paper "A diagrammatic view of differential equations in physics"

    8. 2021

  8. Holomorphic Deligne cohomology
    Stockholm University
    [Slides: PDF]
    Introduction to Deligne cohomology in the complex-analytic setting. Contains quite a few typos and mistakes
  9. Homotopical methods in complex geometry
    Graduate Student Topology And Geometry Conference
    [Slides: PDF]
    Short introduction to the idea of homotopical complex geometry
  10. Simplicial connections and resolutions for coherent analytic sheaves
    Stockholm University
    [Slides: PDF]
    Summary of my PhD thesis work

    11. 2020

  11. Connections and curvature
    [Video: Vimeo]
    Short video series that introduces the idea of connections and curvature using as little actual differential geometry as possible
  12. Simplicial Chern-Weil theory for coherent analytic sheaves
    [Video: YouTube]
    Video summary of my PhD thesis for the Junior Mathematician Research Archive

    13. 2019

  13. Twisting cochains and twisted complexes
    Young Topologists Meeting 2019
    [Slides: PDF]
    An introduction to twisting cochains and twisted complexes in algebraic topology and complex geometry

Teaching and notes