# Marius Leonhardt

If you want to contact me, my email address is mleonhardt (at) mathi (dot) uni-heidelberg (dot) de .

## Research

I am interested in the arithmetic of abelian varieties, especially the theory of complex multiplication, Shimura varieties, and related topics. I also have some interest in cryptography and knot theory.

Since April 2020, I am a “wissenschaftlicher Mitarbeiter” at the University of Heidelberg. Before that I was a PhD student of Tony Scholl at the University of Cambridge.

### Publications

1. Plectic Galois action on CM points and connected components of Hilbert modular varieties, Jan 2020, arXiv, submitted. This article contains the results of my PhD research and is a shortened version of my PhD thesis.

## Teaching

This term (WS 2020/21) I will be Obertutor for the lecture Algebra 1. For details and past teaching, click here.

During my PhD I participated in several reading groups about number-theoretic topics. Details can be found here.

## Talks

Here you can find a list of talks I have given at research seminars and conferences:

• Plectic phenomena on Hilbert modular varieties, seminar talk, Heidelberg, Jan 2020.
• Plectic phenomena on Hilbert modular varieties, Journées Arithmétiques Istanbul, July 2019; similar talks given at Y-RANT Warwick, Nov 2019, and KIT Christmas workshop, Dec 2020. slides
• L-functions of CM elliptic curves, Y-RANT Sheffield, Nov 2018.
• The main theorem(s) of complex multiplication and beyond, Bristol Linfoot Number Theory Seminar, May 2018.
• Snapshots of Complex Multiplication, Lancaster Junior Seminar, Apr 2018.
• CFT of IQNF via EC with CM, TMS symposium, Feb 2018. slides
• CFT of IQNF via EC with CM, PhD student colloquium, Cambridge, Apr 2017. notes
• Recovering a local field from its Galois group, Cambridge number theory seminar, Feb 2017; similar talks given at the Copenhagen number theory seminar, Dec 2016, and Cambridge Kinderseminar, Nov 2016. notes

### Conferences

Here is a list of conferences and workshops I attended/plan to attend.

• British Mathematical Colloquium, Glasgow, UK, April 2020 (upcoming)
• Arithmetic Geometry, Darmstadt, Germany, March 2020 (upcoming)
• Journées Arithmétiques, Istanbul, Turkey, July 2019
• CMI-HIMR Summer School in Computational Number Theory, Bristol, UK, June 2019
• Y-RANT, Sheffield, UK, November 2018
• CMI at 20, Oxford, UK, September 2018
• Journées Arithmétiques, Caen, France, July 2017
• Arizona Winter School, Tucson, USA, March 2017
• $p$-adic methods for Galois representations and modular forms, Barcelona, Spain, February 2017 (including Payman Kassaei’s course on $p$-adic Hilbert modular forms)
• Christmas workshop for Geometry and Number Theory, Karlsruhe, Germany, December 2016
• Galois Representations and Automorphic Forms, Bedlewo, Poland, August 2016
• Crashcourse on Shimura Varieties, Leiden, Netherlands, June 2016
• Christmas workshop for Geometry and Number Theory, Karlsruhe, Germany, December 2015

I am also frequently participating in the ‘Kleine AG’. Topics include for example:

• Lawrence-Venkatesh’s proof of Siegel’s theorem, November 2019
• Serre’s Modularity Conjecture, May 2019 (organised by Christoph Spenke and myself)
• Deligne’s Travaux de Shimura, October 2018
• Falting’s Endlichkeitssätze für Abelsche Varietäten über Zahlkörpern, October 2017
• Tate’s p-divisible groups, February 2017
• The Neukirch-Uchida theorem, June 2015

### Other stuff I have written

(contact me for the pdfs)

• Plectic arithmetic of Hilbert modular varieties, PhD Thesis, University of Cambridge, submitted 07/2019.
• 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 in Cor. 2.8 (copied from Silverman) contains a mistake – before calculating the rank one needs to show that the isogenies form a finitely generated $\mathbb{Z}$-module. This is necessary since otherwise something like $\mathbb{Z}[\frac{1}{p}]$ would have rank $1$. Thanks to Lennart Gehrmann for pointing it out.
• 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.

Thanks to Sam Power for his help and advice on creating this webpage.