I can still reason — I studied mathematics which is the madness of reason — but now I want the plasma — I want to eat straight from the placenta.
—Clarice Lispector
i studied for my DPhil in computer science under Sam Staton at the University of Oxford, as a member of Exeter College.
i am interested in the foundations of probability theory, particularly categorical foundations, with an eye to developing semantics of probabilistic programming languages. in other words, i try to answer three questions with compositional approaches:
what do we mean when we talk about probability?
what do we calculate when we do calculations with probability?
how closely do computers agree with us on our answers to the previous two questions?
more recently, this has involved considering the connections between classical and quantum probability.
my mathematical work is creative; my creative work is influenced by mathematics.
thesis
Summers. N. (2026) Exchangeability Theorems as Categorical Limits of Probabilistic and Quantum Processes. DPhil. Thesis. University of Oxford. available here.
you may read the acknowledgements here.
publications
Selected for QPL plenary:
S. Staton and N. Summers. Quantum de Finetti Theorems as Categorical Limits, and Limits of State Spaces of C*-algebras. In Stefano Gogioso and Matty Hoban: Proceedings 19th International Conference on Quantum Physics and Logic (QPL 2022), Wolfson College, Oxford, UK, 27 June – 1 July 2022, Electronic Proceedings in Theoretical Computer Science 394, pp. 400–414.
Published: 16th November 2023.
DOI: 10.4204/EPTCS.394.19
Plenary Talk: youtube
talks
S. Staton and N. Summers. Exchangeability and the Radon Monad: Probability Measures, Quantum States and Multisets. Presented at Applied Category Theory 2022 (ACT 2022)
Extended Abstract: pdf
Talk: youtube (timestamped at 2:28:19)