# Algebra Seminar 2020/21

Due to the current Covid-19 pandemic, we will host online research talks until further notice. Send an email to steffen.muller@rug.nl if you want to participate.

We meet on Wednesdays.

## Schedule

- 24-02-21, 15:00 Harry Justus Smit (MPIM Bonn): TBA
- 10-02-21, 15:00 Angeliki Mali (Groningen): TBA
- 03-02-21, 17:00 Levent Alpöge (Columbia University): TBA
- 27-01-21, 15:00 Damaris Schindler (Göttingen): On the distribution of Campana points on toric varieties
- Abstract: In this talk we discuss joint work with Marta Pieropan on the distribution of Campana points on toric varieties. We discuss how this problem leads us to studying a generalised version of the hyperbola method, which had first been developed by Blomer and Bruedern. We show how duality in linear programming is used to interpret the counting result in the context of a general conjecture of Pieropan-Smeets-Tanimoto-Varilly-Alvarado.

- 20-01-21, 13:00 Marc Masdeu (Universitat Autònoma de Barcelona): Quaternionic rigid meromorphic cocycles
- Abstract: Rigid meromorphic cocycles were introduced by Darmon and Vonk as a conjectural p-adic extension of the theory of singular moduli to real quadratic base fields. They are certain cohomology classes of SL2(Z[1/p]) which can be evaluated at real quadratic irrationalities and the values thus obtained are conjectured to lie in algebraic extensions of the base field. I will present joint work with X.Guitart and X.Xarles, in which we generalize (and somewhat simplify) this construction to the setting where SL2(Z[1/p]) is replaced by an order in an indefinite quaternion algebra over a totally real number field F. These quaternionic cohomology classes can be evaluated at elements in almost totally complex extensions K of F, and we conjecture that the corresponding values lie in algebraic extensions of K. I will show some new numerical evidence for this conjecture, along with some interesting questions allowed by this flexibility.

- 06-01-21 Francesca Bianchi (Groningen): p-adic heights and p-adic sigma functions on Jacobians of genus 2 curves
- 09-12-20 Valentijn Karemaker (Utrecht): Mass formulae for supersingular abelian threefolds
- 02-12-20 Netan Dogra (King's College): p-adic differential equations and rational points on semistable curves
- 25-11-20 Ziyang Gao (IMJ-PRG): Bounding the number of rational points on curves
- 11-11-20 Rosa Winter (Leiden / MPI Leipzig): Density of rational points on a family of del Pezzo surfaces of degree 1
- 04-11-20 Lazar Radicevic (Cambridge): Explicit realization of elements of the Tate-Shafarevich group constructed from Kolyvagin classes
- 28-10-20 Fabien Pazuki (Copenhagen): Bertini and Northcott
- 21-10-20 Anna Somoza (Rennes): Reduction types of Ciani quartics
- 14-10-20 Berno Reitsma (Groningen): A complete algorithm that computes the rational torsion subgroup for Jacobians of hyperelliptic curves of genus 3
- 07-10-20 Clifford Blakestad (Pohang): On p-adic Weierstrass functions
- 30-09-20 Enis Kaya (Groningen): p-adic integration on curves of bad reduction

# Previous years

- In 2019/20 we studied tropical geometry.
- In 2018/19 we studied classical and p-adic heights.
- In 2017/18 we studied Coleman integration and the theory of isocrystals.