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 ChernWeil theory for coherent analytic sheaves, part II
manuscripta mathematica 2023
10.1007/s00229023014845
2003.10591 [math.AG] 
Simplicial ChernWeil 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

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 [mathph] 
Deep neural networks as nested dynamical systems
David I Spivak, Timothy Hosgood
Published on SIAM News Blog (20211201), 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]
2022
2021
Theses

Chern classes of coherent analytic sheaves: a simplicial approach
tel02882140
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 EGAtranslation project). 
An introduction to quantum information science
qubit.guide
Joint work with Artur Ekert, Alastair Kay, and Chiara Macchiavello: an opensource introductory textbook on the fundamentals of theoretical quantum computing. 
Mathematical dictionary
~/mathsdictionary
An opensource 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". 
Holomorphic Deligne cohomology
Stockholm University
[Slides: PDF]
Introduction to Deligne cohomology in the complexanalytic setting. 
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 ChernWeil 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.
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 infinitycategories
[PDF]
Notes on a talk given by Marco Robalo at the 2017 Derived Algebraic Geometry in Toulouse conference.