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

• 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.