1. Various notions of (co)simplicial (pre)sheaves
    2205.15185 [math.CT]
  2. 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]
  3. 2021
  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 1085
    2107.04832 [cs.IT]
  6. 2020
  7. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
    2003.10591 [math.AG]
    Under review.
  8. Simplicial Chern-Weil theory for coherent analytic sheaves, part I
    2003.10023 [math.AG]
    To appear in BSMF.


  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; online book on the fundamentals and some applications of quantum computing.
  • Mathematical dictionary
    An open-source multilingual dictionary of mathematical terminology, contributed to by many (wonderful) volunteers.

Videos and slides

  1. Diagrammatic differential equations
    Applied Category Theory 2022
    [Slides: PDF]
    Overview of the paper "A diagrammatic view of differential equations in physics".
  2. 2021
  3. Holomorphic Deligne cohomology
    Stockholm University weekly seminar
    [Slides: PDF]
    Introduction to Deligne cohomology in the complex-analytic setting.
  4. Homotopical methods in complex geometry
    Graduate Student Topology And Geometry Conference
    [Slides: PDF]
    Short introduction to the idea of homotopical complex geometry.
  5. Simplicial connections and resolutions for coherent analytic sheaves
    Stockholm University
    [Slides: PDF]
    Summary of my PhD thesis work.
  6. 2020
  7. Connections and curvature
    [Video: Vimeo]
    Short video series that introduces the idea of connections and curvature using as little actual differential geometry as possible.
  8. Simplicial Chern-Weil theory for coherent analytic sheaves
    [Video: YouTube]
    Video summary of my PhD thesis for the Junior Mathematician Research Archive.
  9. 2019
  10. 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.