Research interests
I'm a fourth year PhD student with Jakob Stix in the LOEWE research unit “Uniformized Structures in Arithmetic and Geometry". My research area is Arithmetic Geometry, which roughly deals with questions from number theory using algebro-geometric techniques. In particular, I'm interested in anabelian geometry, i.e. the theory of reconstructing certain varieties from their fundamental group. In my PhD project, I try to understand more about the group of outer automorphisms of the absolute Galois groups of p-adic local fields. In ongoing work with M. Lüdtke and A.Betts, we study S-integral points on the thrice punctured line via the (refined) Chabauty--Kim method, providing new examples of (a version of) the Section Conjecture via this computational approach.
In my master thesis I studied Krull-valuations on function fields of arithmetic surfaces. You can find it here (in German).
Publications
In preparation
L. A. Betts, T. Kumpitsch, M. Lüdtke. Chabauty--Kim and the Selmer Section Conjecture.
Preprints
A. J. Best, L. A. Betts, T. Kumpitsch, M. Lüdtke, A. McAndrew, L. Qian, E. Studnia, Y. Xu. Refined Selmer Equations for the Thrice-Punctured Line in depth two. 2021. arXiv:2106.10145 [math.NT]
Past events
Arizona Winter School 2020: Non-Abelian Chabauty, March 7-11, 2020 (Tucson)
Conference "Women in Algebra and Symbolic Computations" (Poster), December 9-11, 2019 (Bad Dürkheim)
Part of the thematic trimester “Reinventing Rational Points", July 1 – 12, 2019 (IHP, Paris)
CMI-HIMR Summer School in Computational Number Theory, June 17 – 28, 2019 (Bristol)
Pre-School “Analytic and geometric methods for rational points", April 8 – 12, 2019 (CIRM, Luminy)
Arizona Winter School 2019: Topology and Arithmetic, March 2 – 6, 2019 (Tucson)
Chow Lectures by Peter Scholze, November 05 – 07, 2018 (Leipzig)
Utrecht Summer School on Geometry, August 20 – 31. 2018 (Utrecht)
Teaching
| Sommersemester 2022 |
Seminar "Funktionenkörper" (Prof. Jakob Stix) |
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Übungen zur Algebraischen Zahlentheorie III (Prof. Jakob Stix) |
| Wintersemester 2021/22: |
Vorkurs für Mathematikstudierende |
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Übungen zur Elementare Zahlentheorie (Prof. Jakob Stix) |
| Sommersemester 2021: |
Vorkurs für Mathematikstudierende |
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Seminar zur Brauergruppe (Prof. Jakob Stix) |
| Seit Wintersemester 2020/21: |
Betreuung des Lernzentrums Mathematik |
| Sommersemester 2020: |
Seminar zu Darstellungen endlicher Gruppen (Prof. Jakob Stix) |
| Wintersemester 2019/20: |
Übungen zur Algebra (Prof. Jakob Stix) |
| Sommersemester 2019: |
Keine Lehre |
Other activities
Since 2014 I'm involved with the math course at Hessische Schülerakademie (Oberstufe) – a summer program for gifted high school students. You can check out what we did in past courses here (in German). In 2022 we will explore the symmetry of things.
