# Marius Leonhardt

If you want to contact me, my email address is m.leonhardt@dpmms.cam.ac.uk.

## Research

I am a 3rd year 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 reading group on the geometric Satake equivalence, meeting on Mondays, 3pm, in MR3.

Unfortunately, there is no junior reading group accompanying it this term, but we hope to return during the break/Easter term.

For more details on past reading groups, see here.

## Teaching

This term (Lent 2018) I am supervising the part IB course groups, rings and modules.

Past teaching includes examples classes in Lie algebras and supervisions in linear algebra, number fields, and number theory. Details can be found here.

## Talks

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

• 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

## Conferences

Here is a list of conferences and workshops I attended.

• 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:

• Falting’s Endlichkeitssätze für Abelsche Varietäten über Zahlkörpern, October 2017
• Tate’s p-divisible groups, February 2017
• The Neukirch-Uchida theorem, June 2015

## Stuff I have written

(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.

## Miscellaneous

• Knots: In July 2018, Wasilij Barsukow and I will offer a course about Knots – theory meets praxis at the Deutsche Juniorakademie Neuerburg for 7th and 8th grade students.
• Sports: You can regularly find me chasing a ball on a football pitch or a squash court, or when trying to juggle.

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