Cohomology and integration

In these lectures I will describe some of the very rich structure that exists on cohomology groups of algebraic varieties, and explain how to use it to study integrals. This will be a gentle introduction, with only prerequisite a basic understanding of the words in the title.

Depending on the interests of the audience, I will discuss topics in the following non exhaustive list:

• periods;
• mixed Hodge theory;
• positive geometries and canonical forms;
• single-valued integration;
• algebraic Mellin transforms and twisted cohomology;
• regularization of divergent integrals;
• motives, the motivic coaction, and symbols.