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. Primary: 18N50, 14F08, 18F20. Secondary: 18N60, 32C35, 14A30, 32L05

Academic employment

  • Director of Operations 2024 – present Topos Institute
  • Academic visitor 2024 University of Oxford
  • Visiting researcher 2023 Okinawa Institute of Science and Technology
  • Postdoc 2021 – 2023 Stockholms universitet
  • Research associate 2020 – 2023 Topos Institute
  • Contracted researcher 2020 – 2021 Centre for Quantum Technologies
  • Academic visitor 2020 – 2021 University of Oxford
  • Scientist 2019 – 2020 Université de Montpellier

Education

  • 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

    2024
  1. The diagrammatic presentation of equations in categories
    Kevin Arlin, James Fairbanks, Tim Hosgood, Evan Patterson
    2401.09751 [math.CT]
  2. 2023
  3. Simplicial presheaves of Green complexes and twisting cochains
    Timothy Hosgood, Mahmoud Zeinalian
    2308.09627 [math.AG]
  4. 2022
  5. Various notions of (co)simplicial (pre)sheaves
    Communications in Mathematics 32 2024
    10.46298/cm.10359
  6. 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
  7. 2021
  8. 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]
  9. Dirichlet polynomials and entropy
    David I Spivak, Timothy Hosgood
    Entropy 23 2021
    10.3390/e23081085
  10. 2020
  11. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
    manuscripta mathematica 2023
    10.1007/s00229-023-01484-5
  12. 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

Theses

Other work

Teaching

  • Stockholms universitet 2021 – 2023 Masters students
    Commutative algebra and algebraic geometry.
  • University of Oxford 2021, 2024 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

Selected 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: October 2022