Work // Tim Hosgood

Ordered by date of initial arXiv upload, not by date of final publication.

Various notions of (co)simplicial (pre)sheaves
Communications in Mathematics 32 2024
10.46298/cm.10359
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]

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]

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.

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: 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.

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.
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.

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.