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.

Reading Groups

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.