Magma Meeting: Rational Points 2025

Organizers: Stephan Elsenhans, Timo Keller, and John Voight

Supported by the Simons Foundation

Date and Place

July 25 – 26, 2025
in the Humboldt building at Universität Würzburg, Würzburg, Germany

Hotel: Dorint Hotel Würzburg

Schedule

Day 1

• 09:00–09:30: Arrival, coffee
• 09:30–10:00: Opening discussion, setting goals for the meeting
• 10:00–10:15: short break
• 10:15–11:00: talk by Stephan Elsenhans on computing class groups in Magma
• 11:00–11:15: short break
• 11:15–12:00: discussion on number fields and rational points, what's missing, pain points, hacks, desired features.
• 12:00–01:00: glamorous mensa lunch
• 13:00–13:45: report/demo by Michael Stoll on computing rational points on genus 2 curves
• 13:45–14:00: short break
• 14:00–15:00: discussion on infrastructure for rational points, descent, cohomology, elliptic surfaces, ...
• 15:00–15:30: coffee break
• 15:30–17:00: specialized (small group) discussions, feature requests and gaps, research problems, put reports in Overleaf
• 17:30: dinner at Restaurant Hubland

Day 2

• 09:30–10:00: brief recap and outcomes from day 1
• 10:00–11:00: discussion on magma internals, interface design (e.g. varieties, maps between curves; "I can't believe it's not in Magma")
• 11:00–11:15: short break
• 11:15–12:15: editing of Overleaf white paper/report
• 12:15–12:30: conclusion, roadmap; What are the most important takeaways?

Participants

• David Angdinata
• Nils Bruin
• Brendan Creutz
• Maarten Derickx
• Stephan Elsenhans
• Claus Fieker
• Ludwig Fürst
• María Inés de Frutos Fernández
• Naemi Fischer
• Pip Goodman
• Jörg Jahnel
• Timo Keller
• Jürgen Klüners
• Lars Kühne
• Steffen Müller
• Filip Najman
• Oana Padurariu
• Ignasi Sanchez Rodriguez
• Michael Stoll
• John Voight

Aim of the conference

This workshop will focus on the study of rational points on algebraic varieties using computational tools in the Magma computer algebra system. The program will include collaborative discussions on available algorithms, current problems and open questions, feature requests, and design considerations. Such algorithms often rely heavily upon underlying algorithms for extensions of number fields, for example computations of unit groups and class groups. We hope to guide future directions for algorithmic and computational advancements in Magma.

It is a pre-workshop for Rational Points 2025.