I still have the power of reason — I studied mathematics which is the madness of reason — but now I want the plasma — I want to feed directly from the placenta. —Clarice Lispector
i am currently studying for a phd in computer science under sam staton at the university of oxford, as a member of exeter college.
here is my departmental web page.
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.
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)
master’s thesis, 2019: Galois and Tannakian Categories
As with all good mathematics, category theory attempts to create connections between abstract ideas. A way of translating information like this provides free theorems and proofs but far greater than this, it gives us a means to formalise similarities in intuition or indeed form entirely new intuition, useful whether or not an idea is well understood. Category theory does this in such a general way that it may almost been seen as a language. It is only in this language that connections that appear to us intuitively can be made into formal mathematical correspondences. In this project, we will deal with the preliminaries of category theory, with a particular focus on forming examples in the categories of covering spaces for a topological space X, and separable field extensions. It is here we will see how the language of category theory connects these seemingly very separate areas of maths as instances of Galois Categories. With our categorical foundations laid, we will cover an introduction to the theory of affine group schemes and lay out the definition of a neutral Tannakian categories to see how these two areas are related.