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

Education and academic employment

  • Postdoc 2021 – present Stockholms universitet
    Supervised by Wushi Goldring
  • Research associate 2020 – present Topos Institute
    Research associate and web admin
  • Contracted researcher 2020 – 2021 Centre for Quantum Technologies
    Created qubit.guide
  • Academic visitor 2020 – 2021 University of Oxford
    TA for MMath courses
  • Scientist 2019 – 2020 Université de Montpellier
    Part of the DerSympApp ERC project
  • Doctorat en mathématiques 2016 – 2020 Université d'Aix-Marseille
    Supervised by Julien Grivaux and Damien Calaque
  • MMath (Mathematics) 2015 – 2016 University of Oxford
    First-class honours
  • BA (Mathematics) 2012 – 2015 University of Oxford
    Upper second-class honours

Publications and preprints

    2022
  1. Various notions of (co)simplicial (pre)sheaves
    2205.15185 [math.CT]
  2. 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
  3. 2021
  4. 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]
  5. Dirichlet polynomials and entropy
    David I Spivak, Timothy Hosgood
    Entropy 23 2021
    10.3390/e23081085
  6. 2020
  7. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
    2003.10591 [math.AG]
    The second paper extracted from my PhD thesis; under submission.
  8. Simplicial Chern-Weil theory for coherent analytic sheaves, part I
    2003.10023 [math.AG]
    The first paper extracted from my PhD thesis; under submission.

Theses

    2020
  • Chern classes of coherent analytic sheaves: a simplicial approach
    tel-02882140
    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.

Other work

  • Introduction to Quantum Information Science
    qubit.guide
    Joint work with Artur Ekert: an elementary exposition of the fundamentals of theoretical quantum computing.
  • Translations
    thosgood.com/translations
    Various mathematical writings translated into English (including links to the EGA-translation project).

Teaching

  • Stockholms universitet 2021 – 2022 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.

Organisation

  • Topos Institute Colloquium 2021 – present topos.site/topos-colloquium
    Co-organised and run with David Spivak.
  • Em-Cats Virtual Seminar 2021 – 2022 topos.site/em-cats
    Co-organised and run with Eugenia Cheng and Brendan Fong.

Conference and seminar talks

    2022
  • Diagrammatic differential equations
    Applied Category Theory 2022
  • 2021
  • 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)
  • 2020
  • Simplicial connections and resolutions for coherent analytic sheaves
    Stockholm University (online)
  • Connections and curvature
    UGA Graduate Student Seminar (online)
  • 2019
  • Simplicial Chern–Weil Theory
    DerSympApp, Université de Montpellier
  • Twisting cochains and twisted complexes
    Young Topologists Meeting 2019, Lausanne
  • 2018
  • Des méthodes simpliciales pour la géométrie complexe
    Conférence de l'équipe AGT d'Aix-Marseille, Carry-le-Rouet
  • 2017
  • Les classes de Chern des fibrés vectoriels
    Séminaire Géométrie Complexe, Marseille

Other professional experience

  • 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.

  • 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.

CV last updated: April 2022