If you want to contact me, my email address is
*m.leonhardt (at) dpmms (dot) cam (dot) ac (dot) uk*.

I am a PhD student of Tony Scholl, working on Galois actions on abelian varieties with complex multiplication. To be more precise, my research project involves the so-called plectic Galois group, a certain finite index extension of the absolute Galois group of $\mathbb{Q}$, and its action on CM abelian varieties.

This term, I am participating in the number theory reading group on Lawrence-Venkatesh's proof of the Mordell Conjecture (arxiv).

Occasionally we also have a junior study group about Xiao-Zhu's paper on Cycles on Shimura Varieties.

Separate webpage: Reading Groups

This term (Michaelmas 2018) I am giving examples classes to the part III course on Lie algebras. The course webpage is here.

Separate webpage: Teaching

Here you can find a list of talks I have given (apart from the talks held at the reading groups above):

*The main theorem(s) of complex multiplication and beyond*, Bristol Linfoot Number Theory Seminar, May 2018.*Snapshots of Complex Multiplication*, Lancaster Junior Seminar, April 2018.*CFT of IQNF via EC with CM*, TMS symposium, February 2018. slides*CFT of IQNF via EC with CM*, PhD student colloquium, Cambridge, April 2017. notes*Recovering a local field from its Galois group*, Cambridge number theory seminar, February 2017; same talk at the Copenhagen number theory seminar, December 2016, and Cambridge Kinderseminar, November 2016. notes

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

- 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:

*Serre's Modularity Conjecture*, Spring 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)

*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.