I'm a mathematician looking at the interactions of homotopy theory and arithmetic geometry. In particular, I look at ways we can use homotopy theory to approach results in anabelian geometry, arithmetic curve counting, and rational points on varieties. At the moment, the two main things I'm thinking about are anabelian geometry, rational points, and the connections between them, as well as the arithmetic and geometric behaviour of a quadratically enriched Euler characteristic from motivic homotopy.
Since September 2024, I'm based at the University of Bath as a postdoctoral research fellow working with Daniel Loughran. I currently organise the GWNT seminar, a seminar designed to connect number theorists in the south west (applied loosely) of England, along with 6 other people.
From September 2023 to the end of August 2024, I was based at the University of Canterbury in New Zealand as a postdoctoral research fellow on the Marsden grant "Rational Points and Anabelian Geometry", working with Brendan Creutz and Felipe Voloch. Before that I defended my thesis in August 2023 at Imperial College London, supervised by Ambrus Pál, as part of the 2019 cohort of the London School of Geometry and Number Theory.
The papers I've written can be found here. My CV is this link (updated in October 2024), and I'm always happy to answer questions about work in preparation.
The list of talks I've given is here. I enjoy giving talks, so please get in touch if you'd like me to speak about something I've written!
In Autumn 2022, Ambrus Pál and I organised a study group on the series of papers "Smooth Profinite Groups" by de Clercq and Florence for the London Number Theory seminar. For more details click here.
I organised the London Junior Number Theory seminar for the academic year 2020-21 with Soham Karwa. A list of speakers and their abstract for the 2020-21 year can be found here. If you are interested in attending, subscribe to the mailing list.
In Autumn 2020, I also organised a study group on the étale homotopy obstruction to rational points. More details are available here.
You can contact me by email: jp907@bath.ac.uk
My pronouns are he/him.
You can find my office at 1.03 in 6W on the University of Bath campus.
Other Links
My MathSciNet author ID is 1636196
In case you're looking to run into me at a conference
I'll be at the Motives and Arithmetic Geometry conference in Darmstadt from July 28th-August 1st.
I'll be at Geometric and Analytic Number Theory in Bath from the 8th-12th September (though it's unclear whether this is "travel")