The aim of the school is to introduce undergraduate and graduate students to two classical themes in algebraic geometry. It will consist of two lecture courses given by Jarosław Wisniewski and Piotr Achinger.

Each lecture course will be accompanied by exercise sessions, leaving some building blocks and lemmas to be proved by the participants.

Jarosław Wisniewski (University of Warsaw) will give a course on group actions on varieties. The introductory part will be about polynomial invariants of linear actions of finite groups. Next, we shall consider algebraic actions of affine algebraic groups and their quotients. A special consideration will be given to algebraic torus action and quotients. Finally, the lecturer shall focus on applications to birational geometry of projective varieties.

The course is aimed at students who completed commutative algebra lectures (ring and fields) and an introductory course to algebraic geometry.

Piotr Achinger (Kyiv School of Economics & IMPAN Warsaw) will give a first introduction to abelian varieties. Abelian varieties are higher-dimensional analogs of elliptic curves. Over the complex numbers, they can be described as the quotient of C^g by a lattice. The course will first investigate complex abelian varieties, and then study arithmetic aspects of abelian varieties over number fields and finite fields.

Familiarity with basics of algebraic geometry and differential geometry will be required.