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

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.

*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.

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.

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

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
- -adic methods for Galois representations and modular forms, Barcelona, Spain, February 2017 (including Payman Kassaei’s course on -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

(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 -module. This is necessary since otherwise something like would have rank . 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.