## Welcome!

I am currently a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn.

Before I was a post-doc 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 .

I am interested in the Langlands programme via arithmetic geometry.

In particular, I am interested in the

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.## Preprints

On endoscopic

*p*-adic automorphic forms for SL(2), Preprint, 2016.

## Publications

A quotient of the Lubin-Tate tower, 2016, to appear in Forum of Mathematics, Sigma.

*L*-Indistinguishability on Eigenvarieties, 2016, to appear in Journal of the Institute of Mathematics of Jussieu. Journal version.A

*p*-adic Labesse-Langlands transfer, manuscripta mathematica,**154(1-2)**, pp. 23-57, 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.*p*-adic functoriality for inner forms of unitary groups in three variables, Mathematical Research Letters,**21(1)**, pp. 141-148, 2014. Journal version.

Wintersemester 2016/17

Exercises for the course Algebra II .

Arithmetische Geometrie Oberseminar (ARGOS) (with Prof. Peter Scholze):

Arthur's endoscopic classification and level one cusp forms .

Conference on *p*-adic methods for Galois representations and modular forms .

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:**

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.

**Dr. Judith Ludwig**

Max Planck Institute for Mathematics

Office 405, Vivatsgasse 7

53111 Bonn

Germany

Email: ludwig (add @mpim-bonn.mpg.de)

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