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 (Mathematics) 2012 – 2016 University of Oxford
  First-class honours

Publications and preprints

2024

1. The diagrammatic presentation of equations in categories
   Kevin Arlin, James Fairbanks, Tim Hosgood, Evan Patterson
   2401.09751 [math.CT]

2023

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

2022

3. Various notions of (co)simplicial (pre)sheaves
   Communications in Mathematics 32 2024
   10.46298/cm.10359
4. 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

5. 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]
6. Dirichlet polynomials and entropy
   David I Spivak, Timothy Hosgood
   Entropy 23 2021
   10.3390/e23081085

2020

7. Simplicial Chern-Weil theory for coherent analytic sheaves, part II
   manuscripta mathematica 2023
   10.1007/s00229-023-01484-5
8. 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

• University of Oxford 2024 Masters students
  Introduction to quantum information, algebraic topology, algebraic geometry, homological algebra, category theory.
• 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 many other members of the Topos Institute.
• 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

2023

• Geometry-independent constructions of bundles and sheaves
  Topology, Geometry, and Physics Seminar (online)

2022

• Diagrammatic differential equations
  Applied Category Theory 2022

2021

• What is... a quantum algorithm?
  What is... a seminar? (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