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

• 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

• 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

2023

1. Simplicial presheaves of Green complexes and twisting cochains
   Timothy Hosgood, Mahmoud Zeinalian
   2308.09627 [math.AG]

2022

2. Various notions of (co)simplicial (pre)sheaves
   Communications in Mathematics 32 2024
   10.46298/cm.10359
3. 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

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

2020

6. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
   manuscripta mathematica 2023
   10.1007/s00229-023-01484-5
7. 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

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, 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

• 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

• 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

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.