Research
Current research topics. (a) Homotopical and simplicial methods in complex-analytic geometry; coherent analytic sheaves. (b) Chern classes; holomorphic Deligne cohomology. (c) Natural-language translation.
MSC2020. 18N50, 18N60, 32C35, 14F08, 14A30, 18F20, 32L05
Academic employment
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Academic visitor
2023
Okinawa Institute of Science and Technology
Invited by Artur Ekert -
Postdoc
2021 – 2023
Stockholms universitet
Supervised by Wushi Goldring -
Research associate
2020 – present
Topos Institute
Research associate and internal systems admin -
Contracted researcher
2020 – 2021
Centre for Quantum Technologies
Created qubit.guide with Artur Ekert -
Academic visitor
2020 – 2021
University of Oxford
TA for MMath courses -
Scientist
2019 – 2020
Université de Montpellier
Part of the DerSympApp ERC project
Education
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Doctorat (PhD) en mathématiques
2016 – 2020
Université d'Aix-Marseille
Supervised by Julien Grivaux and Damien Calaque -
MMath and BA (Mathematics)
2012 – 2016
University of Oxford
First-class honours, upper second-class honours (resp.)
Publications and preprints
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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 -
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 -
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 -
Simplicial Chern-Weil theory for coherent analytic sheaves, part II
manuscripta mathematica 2023
10.1007/s00229-023-01484-5 -
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
2023
2022
2021
2020
Theses
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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.
2020
2016
Other work
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Introduction to Quantum Information Science
qubit.guide
Joint work with Artur Ekert, Alastair Kay, and Chiara Macchiavello: an introductory textbook on the fundamentals of theoretical quantum computing. -
Translations
thosgood.com/translations
Various mathematical writings translated into English (including links to the EGA translation project).
Teaching
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Stockholms universitet
2021 – 2023
Masters students
Commutative algebra and algebraic geometry. -
University of Oxford
2021
Masters students
Introduction to quantum information, algebraic topology, category theory. -
Université d'Aix-Marseille
2017 – 2019
Undergraduates
Algèbre linéaire, calcul différentiel, maths en anglais. -
Kingsley School, Bideford
2013
Sixth-form
Mathematics and Further Mathematics A-levels.
Event organisation
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Topos Institute Colloquium
2021 – present
topos.site/topos-colloquium
Co-organised and run with David Spivak. -
Virtual Double Categories Workshop
2022
bryceclarke.github.io/virtual-double-categories-workshop
Co-organised and run with Bryce Clarke. -
Em-Cats Virtual Seminar
2021 – 2022
topos.site/em-cats
Co-organised and run with Eugenia Cheng and Brendan Fong.
Selected conference and seminar talks
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Diagrammatic differential equations
Applied Category Theory 2022 -
What is... a quantum algorithm?
What is... a seminar? (online) -
Holomorphic Deligne cohomology
Stockholm University (online) -
Homotopical methods in complex geometry
Graduate Student Topology and Geometry Conference (online) -
Simplicial connections and resolutions for coherent analytic sheaves
Stockholm University (online) -
Connections and curvature
UGA Graduate Student Seminar (online) -
Simplicial Chern–Weil Theory
DerSympApp, Université de Montpellier -
Twisting cochains and twisted complexes
Young Topologists Meeting 2019, Lausanne -
Des méthodes simpliciales pour la géométrie complexe
Conférence de l'équipe AGT d'Aix-Marseille, Carry-le-Rouet -
Les classes de Chern des fibrés vectoriels
Séminaire Géométrie Complexe, Marseille
2022
2021
2020
2019
2018
2017
Other professional experience
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IT technician; help-desk manager
2016
Hertford College, University of Oxford
Led site-based IT development and network infrastructure upgrades. Managed staff and student help desk for the entire college, with responsibilities including hardware repair and software support. Improved registration systems with shell-scripting automation (Ruby, Bash). Various server management and maintenance tasks.
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Network Functions Virtualisation Intern
2014
Metaswitch
Worked as part of the NFV team on the Virtual Route Reflector. Researched and presented information to the whole team on various aspects of network configuration management (e.g. NETCONF, TACACS+) before implementing them. Set up test systems for aforementioned aspects, as well as others. Gained experience with C, Bash, and Python. Completed an Effective Communications course, as well as a three-day hackathon.