picture of cusps

Research interests

I am interested in number theory and arithmetic geometry, particularly in the theory of p-adic automorphic forms and eigenvarieties, as well as Shimura varieties and perfectoid spaces.

For my thesis, I study modular forms at the boundary of weight space (the conjectural "spectral halo") using the "t-adic" modular forms in characteristic p constructed by Andreatta, Iovita and Pilloni. I compare these to p-adic modular forms using perfectoid methods: This is possible because p-adic modular forms are closely related to Scholze's modular curves at infinite level, e.g. by work of Chojecki-Hansen-Johannson.

The diagram on the left illustrates the situation at the cusps of various modular curves of infinite level. This is useful for studying q-expansions of modular forms using infinite level modular curves.

There are many other things I find interesting: There is so much fascinating mathematics out there!

Publications and preprints

Perfectoid geometry of p-adic modular forms. (PhD thesis, available upon request)

q-expansion principles for modular curves at infinite level. preprint

Overconvergent Hilbert modular forms via perfectoid modular varieties (with Christopher Birkbeck and Chris Williams). preprint

Perfectoid covers of abelian varieties (with Clifford Blakestad, Damián Gvirtz, Daria Shchedrina, Koji Shimizu, Peter Wear and Zijian Yao). arxiv.org/abs/1804.04455 (submitted).

Rigid τ-crystals. Journal de Théorie des Nombres de Bordeaux, 29(3):1059-1082, 2017.

All solutions to the immobilizer problem (with John Conway). Math. Intelligencer, 36(4):78-86, 2014.

Proof-reading guidance in cell tracking by sampling tracking-by-assignment models (with Martin Schiegg, Carsten Haubold, Steffen Wolf, Ulrich Koethe and Fred A Hamprecht). In Biomedical Imaging (ISBI), 2015 IEEE 12th International Symposium.