Minimal covolume of the Siegel modular group
Kristian Holm (Universität Kiel)
- https://www.uni-giessen.de/de/fbz/fb07/fachgebiete/mathe/veranstaltungen/wissenschaftliche_veranstaltungen/oberseminar_algebra_geometrie_topologie/termine/holm_2025
- Minimal covolume of the Siegel modular group
- 2025-05-20T16:00:00+02:00
- 2025-05-20T17:30:00+02:00
- Kristian Holm (Universität Kiel)
20.05.2025 von 16:00 bis 17:30 (Europe/Berlin / UTC200)
I will report on recent joint work with Amir Džambić and Ralf Köhl where we prove that, among all lattices in the Lie group Sp(2n, R), the group Sp(2n, Z) has the smallest covolume (and is unique with this property, at least up to conjugation).
I will not cover the whole proof of this theorem, but instead present selected parts of the argument: The proof relies crucially on Prasad's volume formula — a sophisticated result that gives an elaborate expression for the covolume of distinguished arithmetic subgroups of simply connected, absolutely simple algebraic groups defined over number fields. In particular, I will explain how this formula can be used to prove the (arguably, much less abstract) result announced above with the help of classical estimates of global arithmetic invariants of number fields.