Marius Leonhardt

Address:
Ruprecht-Karls-Universität Heidelberg
Institut für Mathematik
Im Neuenheimer Feld 205
69120 Heidelberg

Email: mleonhardt (at) mathi (dot) uni-heidelberg (dot) de
Telephone: +49 6221 54 14841
Room number: 04.232

About me

I am a postdoc (wissenschaftlicher Mitarbeiter) at the University of Heidelberg in the group of Alexander Schmidt. I am part of the project C01 (Tame cohomology of schemes and adic spaces) of the SFB-TRR GAUS. My research focusses on studying rational points with the Chabauty–Kim method. Other research interests include the arithmetic of abelian varieties, especially the theory of complex multiplication, Shimura varieties, and related topics.

Until 2019, I did my PhD under the supervision of Tony Scholl at the University of Cambridge. In my thesis I studied extra “plectic” Galois actions on Hilbert modular varieties.

Before that I completed my studies at the University of Heidelberg (MSc), the University of Cambridge (MAST) and the Karlsruhe Institute of Technology (BSc).

Publications and Preprints

• Linear and quadratic Chabauty for affine hyperbolic curves (with M. Lüdtke and J.S. Müller), Jan 2023, arXiv.
• Towards Uniform Chabauty–Kim (with L.A. Betts and D. Corwin), June 2022, arXiv.
• Plectic Galois action on CM points and connected components of Hilbert modular varieties, Bull. Lond. Math. Soc., 54(6):2254–2277, 2022. http://doi.org/10.1112/blms.12692, arXiv.
• Plectic arithmetic of Hilbert modular varieties, PhD Thesis, University of Cambridge, version 04/2020.

Teaching

This term (SS 2023), I am giving example classes to Galois cohomology 2. As always, the material is on Mampf.

I am also organising a study group (GAUS-AG) on six functor formalism and Poincaré duality. The program is here. If you are interested in participating, please write me an email.

Moreover, I am organising the semi-regular “What is …” seminar. If you would like to give a talk, please write me an email.

• 2023/05/17 … a curve? by myself
• 2023/05/17 … the curve? by Jakob Burgi
• 2023/04/28 … a Drinfeld module? by Oguz Gezmis and Sriram Chinthalagiri Venkata
• 2023/02/17 … a $p$-adic $L$-function? by Max Witzelsperger
• 2023/02/17 … a Sato-Tate-group? by Alireza Shavali

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:

• Effective Chabauty–Kim for CM elliptic curves, Groningen Algebra Seminar, May 2022.
• Plectic Galois action on Hilbert modular varieties, British Mathematical Colloquium, Glasgow (online), Apr 2021.
• 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.

• Journées Arithmétiques, Nancy, July 2023
• An Expedition into Arithmetic Geometry, Leiden, May-June 2023
• Arithmetic Algebraic Geometry, Darmstadt, Oct 2022
• Women in Arithmetic Geometry, Heidelberg, Sept 2022
• Mordell at 100, Cambridge, Aug 2022
• Cohomology of Varieties, Warsaw, Apr 2022
• British Mathematical Colloquium, Glasgow (online), Apr 2021
• Masterclass on Condensed Mathematics, Copenhagen (online), November 2020
• Lean for the curious mathematician, Online, July 2020
• British Mathematical Colloquium, Glasgow, UK, April 2020 (deferred due to the pandemic)
• Arithmetic Geometry, Darmstadt, Germany, March 2020 (deferred due to the pandemic)
• 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)

• 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 of the $\mathbb{Z}$-module of isogenies between two elliptic curves (as presented in Silverman) contains a little gap – one needs to use a bit more about the finitely generated submodules. This is necessary since otherwise something like $\mathbb{Z}[\frac{1}{p}]$ would have rank $1$. Thanks to Lennart Gehrmann for pointing it out. The issue is solved here.
• 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.