Table of contents
2022

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 [mathph]
2021

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
1085
10.3390/e23081085
2107.04832 [cs.IT]
2020

Simplicial ChernWeil theory for coherent analytic sheaves, part II
2003.10591
[math.AG]
Under review.

Simplicial ChernWeil theory for coherent analytic sheaves, part I
2003.10023
[math.AG]
To appear in Bulletin de la Société Mathématique de France.
2020

Chern classes of coherent analytic sheaves: a simplicial approach
tel02882140
PhD thesis; supervised by Julien Grivaux and Damien Calaque.
2016

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 EGAtranslation project).

An introduction to quantum information science
qubit.guide
Joint work with Artur Ekert: 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.
2022

Diagrammatic differential equations
Applied Category Theory 2022
[Slides: PDF]
[Video: YouTube]
Overview of the paper "A diagrammatic view of differential equations in physics".
2021

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.
2020

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.
2019

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.
2021

Teaching materials
~/teaching
Solutions to past exam papers, notes on questions from classes, and small summaries of various concepts.
2017

Robalo's introduction to infinitycategories
[PDF]
Notes on a talk given by Marco Robalo at the 2017 Derived Algebraic Geometry in Toulouse conference.