Abstract for the talk on 30.06.2022 (14:30 h)ICM 2022 preparatory lecture
Stefano Mereta (MPI MiS, Leipzig)
Free resolutions, syzygies, regularity and Betti numbers
30.06.2022, 14:30 h, MPI für Mathematik in den Naturwissenschaften Leipzig, E1 05 (Leibniz-Saal)
In this preparatory lecture I will introduce and state the fundamental properties of some objects and invariants relevant in the study of a module using free resolutions. We will start from the first appearance of these ideas in the work of Hilbert (and even earlier of Cayley), until the recently introduced Boij-Soderberg theory. Time permitting, we will also discuss briefly some bounds and conjectures on the aformentioned invariants.
This is a preparatory lecture for the ICM talk of Irena Peeva.