I am currently an assistant in the Computational Arithmetic Geometry Group at the University of Heidelberg.
Before that I worked as a postdoctoral fellow at the Max Planck Institute for Mathematics and in
the Arithmetic Algebraic Geometry group of the University of Bonn.
In 2014, I completed my Ph.D. at Imperial College London under the supervision of Prof. Kevin Buzzard .
In particular, I am interested in the p-adic and mod p aspects of Langlands functoriality. I like to study p-adic functoriality using non-archimedean geometry, e.g. via eigenvarieties and using the theory of rigid analytic spaces or through towers of (local) Shimura varieties using the theory of perfectoid spaces.
A quotient of the Lubin-Tate tower II (w. Christian Johansson, featuring an appendix by David Hansen), accepted for publication in Mathematische Annalen, 2020.
A inf is infinite dimensional (w. Jaclyn Lang), accepted for publication in Journal of the Institute of Mathematics of Jussieu, 2020.
The Conjectural Relation between Generalized Shalika Models on SO(4n,F) and Symplectic Linear Models on Sp(4n,F): A Toy Example (with Agnès David and Marcela Hanzer), in Women in Numbers Europe: Research Directions in Number Theory, Springer, 2015. Proceedings.
p-adic functoriality for inner forms of unitary groups in three variables, Mathematical Research Letters, 21(1) , pp. 141-148, 2014. Journal version.
Seminar on Derived categories and algebraic geometry.
AG-Seminar on Higher Hida Theory.
Seminar on Elliptic Curves.
Exercises for the course Algebra II (Algebraic Number Theory).
Arithmetische Geometrie Oberseminar (ARGOS) (with Prof. Peter Scholze):
Arthur's endoscopic classification and level one cusp forms .
I will give a minicourse at the 2020 PIMS - Germany Summer School on Eigenvarieties (postponed to 2021).
I will be a project group leader at Women in Numbers Europe 4 (Utrecht, 2022).
I recently gave a talk in the seminar Recent Advances in Modern p-Adic Geometry. Here are the notes and a link to the recording.
Here are lecture notes from an (online) course on adic spaces and the eigenvariety machine.
In 2019, I assisted a course on adic spaces. Here is a collection of exercises, that might be useful if you are learning the theory.
In August 2016, I gave a Minicourse on Mod p Langlands correspondences via arithmetic geometry at KIAS. You can find notes of this course here .
Summary of my lectures on p-divisible groups (2019).
Here is a poster explaining the results of my paper "L-Indistinguishability on Eigenvarieties".
Here is a motivational poster giving a brief introduction to the Langlands programme, aimed at master students.
IWR (Interdisciplinary Center for Scientific Computing)
University of Heidelberg
Im Neuenheimer Feld 205
Email: judith.ludwig (add @iwr.uni-heidelberg.de)