There will be some occassional series of lectures given by our Mercator-Fellows and some selected guests.

On May 2025 our Mercator-Fellow Olivier Benoist will hold a series of lectures on "Real algebraic geometry and Hodge Theory".

Abstract: Many questions in real algebraic geometry are influenced by the cohomology and the Hodge theory of the real algebraic varieties under investigation. In this series of lectures, I will give an introduction to this theme (the cohomological study of real algebraic varieties). I will then apply these techniques to several classical problems (algebraic approximation questions, sums of squares problems, the period-index problem...).

The lectures will take place each Tuesday of May from 14:15 to 15:45 (with a short pause in between) in the room F107 of the main building of Leibniz University Hannover.

Here is a temptative plan for the talks:

1. Introduction to real algebraic geometry (May 6, 14:15 - 15:00).

2. Equivariant cohomology and the real cycle class map (May 6, 15:00 - 15:45).

3. Hodge theory of real algebraic varieties (May 13, 14:15 - 15:00).

4. Connection with sums of squares and approximation problems (May 13, 15:00 - 15:45).

5. The case of surfaces with vanishing geometric genus (May 20, 14:15 - 15:00).

6. Real Noether-Lefschetz loci (May 20, 15:00 - 15:45).

7. Application to the real integral Hodge conjecture (May 27, 14:15 - 15:00).

8. Application to the period-index problem (May 27, 15:00 - 15:45).

The lectures will be recorded (except the first one). The videos can be found here.