Articles

  1. Various notions of (co)simplicial (pre)sheaves
    (2022)
    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
    10.3934/mine.2023036
    2204.01843 [math-ph]
  3. 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]
  4. Dirichlet polynomials and entropy
    David I Spivak, Timothy Hosgood
    Entropy 23 2021 1085
    10.3390/e23081085
    2107.04832 [cs.IT]
  5. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
    (2020)
    2003.10591 [math.AG]
    The second paper extracted from my PhD thesis; under submission.
  6. Simplicial Chern-Weil theory for coherent analytic sheaves, part I
    (2020)
    2003.10023 [math.AG]
    The first paper extracted from my PhD thesis; under submission.

Theses

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

Projects

  • Translations
    ~/translations
    Various mathematical writings translated into English (including links to the EGA-translation project).
  • An introduction to quantum information science
    qubit.guide
    Joint work with Artur Ekert; online book on the fundamentals and some applications of quantum computing.
  • Mathematical dictionary
    ~/maths-dictionary
    An open-source multilingual dictionary of mathematical terminology, contributed to by many (wonderful) volunteers.

Videos

  • Connections and curvature
    [Vimeo]
    An introduction to connections and curvature that tries to minimise the amount of actual differential geometry used.
  • Simplicial Chern-Weil theory for coherent analytic sheaves (2020)
    [YouTube]
    Summary of my PhD thesis for the Junior Mathematician Research Archive.

Teaching and notes

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