Link to personal website

https://sites.google.com/view/stevengroenLink opens in a new window

Profile

Since September 2019, I'm a PhD student in the number theory group under the supervision of Dr Damiano Testa. My interests include arithmetic geometry and algebraic number theory. My research is mostly in p-torsion of abelian varieties in characteristic p, but also in elliptic curves and arithmetic statistics in positive characteristic.

Contact information

Email: [first name].[last name]@warwick.ac.uk

Office: B0.16, Zeeman Building.

Publications and preprints

Powers of the Cartier operator on Artin-Schreier covers, August 2022, https://arxiv.org/abs/2208.06504Link opens in a new window (under review). CodeLink opens in a new window.

Doubly isogenous genus-2 curves with D4-action, joint with Vishal Arul, Jeremy Booher, Everett W. Howe, Wanlin Li, Vlad Matei, Rachel Pries and Caleb Sringer, February 2021, https://arxiv.org/abs/2102.11419 (under review).

A parametrized set of explicit elements of $\Sha(E/\mathbb{Q})[3]$, joint with Jaap Top, November 2020, https://arxiv.org/abs/2102.11737 (under review).

Teaching

2021-2022: MA426 Elliptic Curves, MA3D5 Galois TheoryLink opens in a new window supervision of first year students.

2020-2021: MA3D5 Galois Theory.

Talks (past and future)

p-Torsion of Artin Schreier covers in characteristic p, University of Arizona, 17 January 2023.

p-Torsion of Artin-Schreier covers in characteristic p, University of Florida, 9-14 January 2023 (precise date not yet known).

p-Torsion of Artin-Schreier covers in characteristic p, Joint Mathematics Meeting, Boston, 4-7 January 2023.

p-Torsion in characteristic p of Jacobians of Artin-Schreier covers, Young Researchers in Algebraic Number Theory conference, University of Glasgow, 23 August 2022.

p-Torsion of Jacobians of curves in Characteristic p, Algebra and Number Theory seminar, University of Groningen, 29 March 2022.

Can you hear the shape of a curve?, postgraduate seminar, University of Warwick, 16 February 2022.

The p-torsion of Jacobians of Artin-Schreier curves, Young Researchers in Algebraic Number Theory conference, University of Bristol (online), 19 August 2021.

A postgrad presentation on p-torsion in characteristic p, postgraduate seminar, University of Warwick, 12 May 2021.

A unique pair of triangles, postgraduate seminar, University of Warwick, 26 February 2020.

Descent by 3-isogeny on elliptic curves, Young Researchers in Algebraic Number Theory conference, University of Warwick, 7 November 2019.

Descent by 3-isogeny on elliptic curves, master's thesis presentation, University of Groningen, 11 July 2019.

Matiyasevich's Theorem: diophantine descriptions of recursively enumerable sets, bachelor's thesis presentation, University of Groningen, 3 July 2017.

Conferences attended

Curves over finite fields and arithmetic of K3 surfaces, University of Groningen, 30 August - 1 September 2022.

Young Researchers in Algebraic Number Theory, University of Glasgow, 23-25 August 2022.

Mordell 2022, University of Cambridge, 15-19 August 2022.

Young Researchers in Algebraic Number Theory, University of Bristol (online), 18-20 August 2021.

Arithmetic, Geometry, Cryptography and Coding Theory, online, 31 May - 4 June 2021.

Algorithmic Number Theory Symposium, online, 30 June - 4 July 2020.

ICERM Workshop on Arithmetic Geometry, Providence USA (online), 1-6 June 2020.

ROW seminar, University of Oxford, 28 January 2020.

Young Researchers in Algebraic Number Theory conference, University of Warwick, 8-11 November 2019.

CMI-HIMR Summer School in Computational Number Theory, University of Bristol, 17-28 June 2019.

Reading groups

The Weil conjectures, 2022

Complex and real multiplication, 2021

Shimura varieties, 2021

Mukai's classification of Fano 3-folds, 2021

Modular forms, 2021

Class field theory, 2020

Algebraic groups, 2020

Derived category, 2020

Perfectoid spaces, 2020

Lazarsfeld's Positivity in Algebraic Geometry, 2020

Tao's algebraic regularity lemma, 2020

Hodge-Tate representations, 2019

Heights, 2018-2019