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.