# November 4-8, 2024 in Groningen, the Netherlands

The workshop is aimed at young researchers such as PhD students and postdocs, and it features three mini-courses on different aspects of rational points.

## Location:

Room 105 in the Bernoulliborg, Zernike Campus, Groningen, the Netherlands.

## Mini-courses by:

Damaris Schindler (Universität Göttingen) Counting techniques for rational points

The goal of this mini-course is to introduce techniques from analytic number theory which are useful in the study of rational points on varieties. This will include a short introduction to the Hardy-Littlewood circle method and if time permits, we will discuss examples, where sieve methods and methods from additive combinatorics can be used in the context of counting rational points on varieties.

Anthony Várilly-Alvarado (Rice University) Vojta’s Conjecture: Motivation and Applications

In the 1980s and 1990s, Vojta laid out variations of a far-reaching conjecture about the distribution of algebraic points on smooth projective varieties over number fields, based on a compelling dictionary between complex analytic objects and number theoretic objects, and on theorems in the complex world by Nevanlinna. Vojta’s insights, while still out of reach, imply and connect many long-standing conjectures in Arithmetic Geometry (Lang, abc, some cases of Manin, etc). In this course, I hope to introduce Vojta’s incredible vision to a new generation of arithmetic geometers.

Bianca Viray (University of Washington) Algebraic points on curves

In this lecture series, we will describe how the Abel-Jacobi morphism gives a geometric framework for algebraic points on a curve of fixed degree. We will review how Faltings’s theorem on rational points on subvarieties of abelian varieties has implications for low degree points on curves and how it gives a division of the algebraic points into so-called parameterized and isolated points. We will also describe how the P^1-parametrizations can be used to describe local splitting conditions of the residue fields of closed points.

## Program:

The workshop will start at 10:45 on Monday morning and will end around lunch time on Friday. There will be research talks on Friday afternoon. The detailed program will follow.

## Registration

Registration is free but mandatory.

- Registration form (deadline October 1, 2024 if you don’t apply for financial support; June 23, 2024 if you do)
- Financial support form (deadline June 23, 2024)

## Code of conduct

## Poster

## Organizers:

Martin Bright, Valentijn Karemaker, Ronald van Luijk, Steffen Müller, Marta Pieropan, Cecília Salgado.