My research focuses on studying rational points on curves with the Chabauty–Kim method. I also work on the geometry and arithmetic of (semi-)abelian varieties.
Publications:
Bounds on the Chabauty–Kim locus of hyperbolic curves (with L.A. Betts and D. Corwin), 2024, Int. Math. Res. Not. IMRN, https://doi.org/10.1093/imrn/rnae067 arXiv.
Linear and quadratic Chabauty for affine hyperbolic curves (with M. Lüdtke and J.S. Müller), 2023, Int. Math. Res. Not. IMRN, https://doi.org/10.1093/imrn/rnad185, arXiv.
Plectic Galois action on CM points and connected components of Hilbert modular varieties, 2022, Bull. Lond. Math. Soc. http://doi.org/10.1112/blms.12692, arXiv.
Plectic arithmetic of Hilbert modular varieties, PhD Thesis, University of Cambridge, version 04/2020.
Undergraduate theses, notes of talks, and other things I wrote: (contact me for pdfs; apologies for the broken links to my previous webpage at Heidelberg)
Hodge-Tate sections, summary of my talk at the GAUS AG on Mochizuki’s proof of the Hom-conjecture, 19/12/2024, Frankfurt.
Complex Multiplication, notes of an overview talk I gave as part of the GAUS AG on Rigid Meromorphic Cocycles, 27/10/2023.
The main theorems of complex multiplication, Smith-Knight and Rayleigh Knight Prize Essay, University of Cambridge, 01/2017.
Galois characterization of local fields, master thesis, University of Heidelberg, supervised by Alexander Schmidt, 09/2015; in German; English summary here.
The Tate-module and the Weil pairing of an elliptic curve, seminar write-up, University of Heidelberg, supervised by Oliver Thomas and Kay Wingberg, 07/2015; in German; notes here. The rank calculation of the Z-module of isogenies between two elliptic curves (as presented in Silverman) contains a little gap – one needs to use a bit more about the finitely generated submodules. This is necessary since otherwise something like Z[1/p] would have rank 1. Thanks to Lennart Gehrmann for pointing it out. The issue is solved here.
p-adic L-functions, part III essay, University of Cambridge, supervised by Tony Scholl, 05/2014.
Minkowski’s existence and uniqueness theorem for surface area measures, bachelor thesis, University of Karlsruhe, supervised by Daniel Hug, 07/2012.