## Adic Spaces I

We will recall the definition and some properties of Huber rings and we will define and study spaces of continuous valuations.

## Adic Spaces II: Examples

We will explain in detail some examples of affinoid adic spaces including the unit ball (for rank 1 valuations). If time permits we will talk on completion and rational subsets.

## Arithmetic Okounkov bodies I

We will review the construction of Newton-Okounkov bodies by Kaveh-Khovanskii and Lazarsfeld-Mustata, within a general framework of semigroups and cones associated to filtrations.

## Arithmetic Okounkov bodies II

We will address the construction of arithmetic Newton-Okounkov bodies, and more generally functions on Newton-Okounkov bodies arising from filtrations, following ideas of Boucksom and collaborators.

## Arithmetic Okounkov bodies III

In the third talk we will continue the discussion of arithmetic Newton-Okounkov bodies and more.

## Perfectoid spaces I

Perfectoid spaces are specially interesting instances of adic spaces.

## Positividad aritmética sobre variedades tóricas

## Espais àdics feixistes

Estudiarem com definir un candidat a feix estructural per a un espai afinoide (de la forma Spa(A,A^+)) i en quins casos surt un feix.

## What is…a Darmon point?

The theory of Heegner points, which form a supply of algebraic points on a given elliptic curve, are one of the main tools used in proving the known cases of the Birch and Swinnerton-Dyer conjecture.