Minicourse 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.

This activity is part of the ERC Synergy Grant UNIVERSE+ www.positive-geometry.com, funded by the European Union (ERC, UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.