Research

Current research. (a) Topological methods and simplicial constructions in complex-analytic geometry, with a focus on coherent sheaves. (b) Language-independent approaches to written mathematics, with an aim towards formal translation via a categorical framework.

Research interests. Homotopical methods in algebraic and complex geometry, simplicial category theory, a formal approach to language translation.

Education and academic employment

  • Research associate, Topos Institute
    2020 – current
    [More information to follow soon]
  • Postdoctoral contractor, Centre for Quantum Technologies
    2020 – current
    Working with Artur Ekert
  • Scientist, Université de Montpellier
    2019 – 2020
    Part of the DerSympApp ERC project
  • Doctorat (PhD) 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. Simplicial Chern-Weil theory for coherent analytic sheaves, part II (2020)
    arXiv:math.AG/2003.10591
    The second paper extracted from my PhD thesis; under submission.
  2. Simplicial Chern-Weil theory for coherent analytic sheaves, part I (2020)
    arXiv:math.AG/2003.10023
    The first paper extracted from my PhD thesis; under submission.

Theses

  • Chern classes of coherent analytic sheaves: a simplicial approach (2020)
    HAL: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)
    arXiv:math.AT/1609.00920
    Secondary master's thesis; unsupervised.

Other output

  • Translations
    https://thosgood.com/translations/
    Various mathematical writings translated into English (including links to the EGA-translation project).
  • An introduction to quantum information science
    thosgood.com/quantum-info
    Joint work with Artur Ekert: an elementary exposition of the fundamentals of theoretical quantum computing.

Teaching

  • Quantum Information Science, University of Oxford
    2021
    4th-year students (masters), in English
    Introductory quantum computing and quantum information theory.
  • Maths en anglais, Université d'Aix-Marseille
    2018 – 2019
    3rd-year undergraduates, in English
    Real analysis, with the aim of improving the mathematical English of French students.
  • Calcul différentiel, Université d'Aix-Marseille
    2018 – 2019
    2nd-year undergraduates, in French
    Basic topology and multivariable calculus.
  • Algèbre linéaire, Université d'Aix-Marseille
    2017 – 2018
    2nd-year undergraduates, in French
    Vector spaces, eigenspaces, and Jordan normal form.
  • Further Mathematics A-level, Kingsley School, Bideford
    2013
    Sixth-form, in English
    FP1, FP2, and D2 (Edexcel)
  • Mathematics A-level, Kingsley School, Bideford
    2013
    Sixth-form, in English
    C1, C2, C3, C4, D1, and M1 (Edexcel)

Conference and seminar talks

  • Homotopical methods in complex geometry
    2021
    Graduate Student Topology and Geometry Conference (online)
  • Simplicial connections and resolutions for coherent analytic sheaves
    2020
    Stockholm University (online)
  • Connections and curvature
    2020
    UGA Graduate Student Seminar (online)
  • Simplicial Chern-Weil Theory
    2019
    DerSympApp, Université de Montpellier
  • Twisting cochains and twisted complexes
    2019
    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: January 2021