Research

Current research. (a) Homotopical and simplicial methods in complex-analytic geometry; coherent analytic sheaves; holomorphic Deligne cohomology. (b) Language-independent approaches to written mathematics; formal translation via a categorical framework.

Research interests. Homotopical methods in complex geometry, (higher) category theory, translation & accessibility. (MSC2020, in numerical order: 14F08, 14F43, 18F20, 18N60, 32C35, 32L05).

Education and academic employment

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

Papers and preprints

  1. A diagrammatic view of differential equations in physics
    Evan Patterson, Andrew Baas, Timothy Hosgood, James Fairbanks
    (2022)
    2204.01843 [math-ph]
  2. Deep neural networks as nested dynamical systems
    joint with David I Spivak
    Published on SIAM News Blog (2021-12-01), available here.
    2111.01297 [cs.LG]
  3. Dirichlet polynomials and entropy
    joint with David I Spivak
    Entropy 23 2021 1085
    10.3390/e23081085
  4. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
    (2020)
    2003.10591 [math.AG]
    The second paper extracted from my PhD thesis; under submission.
  5. Simplicial Chern-Weil theory for coherent analytic sheaves, part I
    (2020)
    2003.10023 [math.AG]
    The first paper extracted from my PhD thesis; under submission.

Theses

  • Chern classes of coherent analytic sheaves: a simplicial approach (2020)
    tel-02882140
    PhD thesis; supervised by Julien Grivaux and Damien Calaque.
  • Under Spec Z: a reader's companion (2016)
    [PDF]
    Primary master's thesis; supervised by Kobi Kremnitzer and Christopher Hollings.
  • Death and extended persistence in computational algebraic topology (2016)
    1609.00920 [math.AT]
    Secondary master's thesis; unsupervised.

Other work

  • An 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
    4th-year students (masters), in English
    Commutative algebra and algebraic geometry.
  • University of Oxford
    2021
    4th-year students (masters), in English
    Introduction to quantum information, algebraic topology, category theory.
  • Université d'Aix-Marseille
    2017 – 2019
    2nd- and 3rd-year undergraduates, in French
    Algèbre linéaire, calcul différentiel, maths en anglais.
  • Kingsley School, Bideford
    2013
    Sixth-form, in English
    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

  • What is... a quantum algorithm?
    2021
    What is... a seminar? (online)
  • Holomorphic Deligne cohomology

    Stockholm University (online)
  • Homotopical methods in complex geometry

    Graduate Student Topology and Geometry Conference (online)
  • Simplicial resolutions for coherent analytic sheaves
    2020
    Stockholm University (online)
  • Connections and curvature

    UGA Graduate Student Seminar (online)
  • Simplicial Chern-Weil Theory
    2019
    DerSympApp, Université de Montpellier
  • Twisting cochains and twisted complexes

    Young Topologists Meeting, Lausanne
  • Des méthodes simpliciales pour la géométrie complexe
    2018
    Conférence de l'équipe AGT d'Aix-Marseille, Carry-le-Rouet
  • Les classes de Chern des fibrés vectoriels
    2017
    Séminaire Géométrie Complexe, Marseille

Other professional experience

  • IT technician; help-desk manager, Hertford College, Oxford
    2016

    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, Metaswitch
    2014

    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