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
-
The diagrammatic presentation of equations in categories
Kevin Arlin, James Fairbanks, Tim Hosgood, Evan Patterson
2401.09751 [math.CT] -
Simplicial presheaves of Green complexes and twisting cochains
Timothy Hosgood, Mahmoud Zeinalian
2308.09627 [math.AG] -
Various notions of (co)simplicial (pre)sheaves
Communications in Mathematics 32 2024
10.46298/cm.10359 -
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 -
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] -
Dirichlet polynomials and entropy
David I Spivak, Timothy Hosgood
Entropy 23 2021
10.3390/e23081085 -
Simplicial Chern-Weil theory for coherent analytic sheaves, part II
manuscripta mathematica 2023
10.1007/s00229-023-01484-5 -
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
2024
2023
2022
2021
2020
Theses
-
Chern classes of coherent analytic sheaves: a simplicial approach
tel-02882140
PhD thesis; supervised by Julien Grivaux and Damien Calaque. -
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.
2020
2016
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
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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
-
Geometry-independent constructions of bundles and sheaves
Topology, Geometry, and Physics Seminar (online) -
Diagrammatic differential equations
Applied Category Theory 2022 -
What is... a quantum algorithm?
What is... a seminar? (online) -
Homotopical methods in complex geometry
Graduate Student Topology and Geometry Conference (online) -
Simplicial connections and resolutions for coherent analytic sheaves
Stockholm University (online) -
Connections and curvature
UGA Graduate Student Seminar (online) -
Simplicial Chern–Weil Theory
DerSympApp, Université de Montpellier -
Twisting cochains and twisted complexes
Young Topologists Meeting 2019, Lausanne -
Des méthodes simpliciales pour la géométrie complexe
Conférence de l'équipe AGT d'Aix-Marseille, Carry-le-Rouet -
Les classes de Chern des fibrés vectoriels
Séminaire Géométrie Complexe, Marseille