Welcome!
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 padic and mod p aspects of Langlands functoriality. I like to study padic functoriality using nonarchimedean 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.
Preprints
Endoscopy on SL(2)Eigenvarieties (w. Christian Johansson), preprint, 2022.
Publications
A quotient of the LubinTate 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.
A quotient of the LubinTate tower, Forum of Mathematics, Sigma, e17, 41pp., 2017. Journal version.
On endoscopic padic automorphic forms for SL(2), Documenta Mathematica, 23, pp. 383406, 2018. Journal version.
LIndistinguishability on Eigenvarieties, Journal of the Institute of Mathematics of Jussieu, 17(2), pp. 425440, 2018. Journal version.
A padic LabesseLanglands transfer, manuscripta mathematica, 154(12), pp. 2357, 2017. Journal version.
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.
padic functoriality for inner forms of unitary groups in three variables, Mathematical Research Letters, 21(1) , pp. 141148, 2014. Journal version.
Summersemester 2021

Seminar on Derived categories and algebraic geometry.
AGSeminar on Higher Hida Theory.

Seminar on Elliptic Curves.

Lecture course Adic Spaces 2.0 . ( Lecture notes ).

Assistant of lecture course Algebra 1 .
Assistant of lecture course Adic spaces 1 (Here are some exercises).

Lecture course on pdivisible groups .
AGSeminar on The FarguesFontaine curve.
Seminar on Representation theory of GL(2) .
AGSeminar on local GShtukas .
Exercises for the course Algebra II (Algebraic Number Theory).
Wintersemester 2015/16
Arithmetische Geometrie Oberseminar (ARGOS) (with Prof. Peter Scholze):
Arthur's endoscopic classification and level one cusp forms .
Upcoming:
I will be a project group leader at Women in Numbers Europe 4 (Utrecht, 2022).
I am coorganizing a spring school on
NonArchimedean Geometry and Eigenvarietes (Heidelberg, 2023).
Notes:
I recently gave a talk in the seminar Recent Advances in Modern pAdic 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 .
Posters:
Summary of my lectures on pdivisible groups (2019).
Here is a poster explaining the results of my paper "LIndistinguishability 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
69120 Heidelberg
Germany
Email: judith.ludwig (add @iwr.uniheidelberg.de)