Research

Current research. (a) Topological methods and simplicial constructions in complex-analytic geometry, with a focus on coherent sheaves. Following on from work by Brylinski and McLaughlin; Grivaux; O’Brian, Toledo, and Tong; Green; and others. (b) Language-independent approaches to written mathematics, with an aim towards formal translation via a categorical framework.

Research interests. Topological complex-analytic geometry, homotopical methods in algebraic geometry, higher category theory, quantum computing, a formal approach to language translation.

Education and academic employment

• Scientist, Université de Montpellier
  2019 – 2020
  Part of the DerSympApp project (ERC 768679)
• Doctorant en maths, Université d'Aix-Marseille
  2016 – 2020
  PhD student under 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
• A-levels and GCSEs, Kingsley School
  2006 – 2012
  Grades A* and A

Papers and preprints

1. Simplicial Chern-Weil theory for coherent analytic sheaves, part I. 2020. math.AG/2003.10023.
   The first paper extracted from my PhD thesis; under submission.
2. Simplicial Chern-Weil theory for coherent analytic sheaves, part II. 2020. math.AG/2003.10591.
   The second 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. math.AT/1609.00920.
  Secondary master's thesis; unsupervised.

Translations and more

• Various mathematical translations.
  https://thosgood.com/translations/
  Includes links to the EGA translation project.

Teaching

• 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

• Connections and curvature
  2020
  UGA Graduate Student Seminar, via Zoom
• 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.