Table of contents


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
    2308.09627 [math.AG]
  2. 2022
  3. Various notions of (co)simplicial (pre)sheaves
    Communications in Mathematics 32 2024
    2205.15185 [math.CT]
  4. 2020
  5. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
    manuscripta mathematica 2023
    2003.10591 [math.AG]
  6. Simplicial Chern-Weil theory for coherent analytic sheaves, part I
    Bulletin de la Société Mathématique de France 151 2023 127–170
    2003.10023 [math.AG]
(Applied) Category Theory
  1. The diagrammatic presentation of equations in categories
    Kevin Arlin, James Fairbanks, Tim Hosgood, Evan Patterson
    2401.09751 [math.CT]
  2. 2022
  3. A diagrammatic view of differential equations in physics
    Evan Patterson, Andrew Baas, Timothy Hosgood, James Fairbanks
    Mathematics in Engineering 5 2022
    2204.01843 [math-ph]
  4. 2021
  5. 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]
  6. Dirichlet polynomials and entropy
    David I Spivak, Timothy Hosgood
    Entropy 23 2021
    2107.04832 [cs.IT]


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


  • Translations
    Various mathematical writings translated into English (including links to the EGA-translation project).
  • An introduction to quantum information science
    Joint work with Artur Ekert, Alastair Kay, and Chiara Macchiavello: an open-source introductory textbook on the fundamentals of theoretical quantum computing.
  • Mathematical dictionary
    An open-source multilingual dictionary of mathematical terminology, contributed to by many (wonderful) volunteers.

Videos and slides

  • Diagrammatic differential equations
    Applied Category Theory 2022
    [Slides: PDF] [Video: YouTube]
    Overview of the paper "A diagrammatic view of differential equations in physics".
  • 2021
  • Holomorphic Deligne cohomology
    Stockholm University
    [Slides: PDF]
    Introduction to Deligne cohomology in the complex-analytic setting. Contains some typos/mistakes.
  • Homotopical methods in complex geometry
    Graduate Student Topology And Geometry Conference
    [Slides: PDF]
    Short introduction to the idea of homotopical complex geometry.
  • Simplicial connections and resolutions for coherent analytic sheaves
    Stockholm University
    [Slides: PDF]
    Summary of my PhD thesis work.
  • 2020
  • Connections and curvature
    [Video: Vimeo]
    Short video series that introduces the idea of connections and curvature using as little actual differential geometry as possible.
  • Simplicial Chern-Weil theory for coherent analytic sheaves
    [Video: YouTube]
    Video summary of my PhD thesis for the Junior Mathematician Research Archive.
  • 2019
  • 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

  • Teaching materials
    Solutions to past exam papers, notes on questions from classes, and small summaries of various concepts.
  • 2017
  • Robalo's introduction to infinity-categories
    Notes on a talk given by Marco Robalo at the 2017 Derived Algebraic Geometry in Toulouse conference.