Work
Table of contents
Articles
Ordered by date of initial arXiv upload, not by date of final publication.
Geometry and Topology
-
Simplicial presheaves of Green complexes and twisting cochains
Timothy Hosgood, Mahmoud Zeinalian
2308.09627 [math.AG] -
Various notions of (co)simplicial (pre)sheaves
Communications in Mathematics 32 2024
10.46298/cm.10359
2205.15185 [math.CT] -
Simplicial Chern-Weil theory for coherent analytic sheaves, part II
manuscripta mathematica 2023
10.1007/s00229-023-01484-5
2003.10591 [math.AG] -
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]
2023
2022
2020
(Applied) Category Theory
-
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 -
The diagrammatic presentation of equations in categories
Kevin Arlin, James Fairbanks, Tim Hosgood, Evan Patterson
2401.09751 [math.CT] -
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] -
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] -
Dirichlet polynomials and entropy
David I Spivak, Timothy Hosgood
Entropy 23 2021
10.3390/e23081085
2107.04832 [cs.IT]
2025
2024
2022
2021
Theses
-
Chern classes of coherent analytic sheaves: a simplicial approach
tel-02882140
PhD thesis; supervised by Julien Grivaux and Damien Calaque. -
Under Spec Z: a reader's companion
[PDF]
Primary master's thesis; supervised by Kobi Kremnitzer and Christopher Hollings. -
Death and extended persistence in computational algebraic topology
1609.00920 [math.AT]
Secondary master's thesis; unsupervised. -
An introduction to varieties in weighted projective space
1604.02441 [math.AG]
Undergraduate project supervised by Balázs Szendrői; sincere caveat lector.
2020
2016
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, Alastair Kay, and Chiara Macchiavello: an open-source introductory textbook on the fundamentals of theoretical quantum computing. -
Mathematical dictionary
~/maths-dictionary
An open-source multilingual dictionary of mathematical terminology, contributed to by many (wonderful) volunteers.
Videos and slides
-
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". -
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 -
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. -
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. -
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. -
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. -
Diagrammatic differential equations
Applied Category Theory 2022
[Slides: PDF] [Video: YouTube]
Overview of the paper "A diagrammatic view of differential equations in physics". -
Holomorphic Deligne cohomology
Stockholm University
[Slides: PDF]
Introduction to Deligne cohomology in the complex-analytic setting. Contains quite a few typos and 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. -
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. -
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.
2026
2025
2024
2022
2021
2020
2019
Teaching and notes
-
Teaching materials
~/teaching
Solutions to past exam papers, notes on questions from classes, and small summaries of various concepts. -
Robalo's introduction to infinity-categories
[PDF]
Notes on a talk given by Marco Robalo at the 2017 Derived Algebraic Geometry in Toulouse conference.