Speaker: Pedro Montero Silva
Date: 10:30 01/04/2022
Title: Intermediate Jacobians and Automorphisms of smooth hypersurfaces of the projective space

Abstract :
Smooth hypersurfaces are classical objects in algebraic geometry since they are the simplest varieties one can define as they are given by only one equation. 
As such, they have been intensively studied and their geometry has shaped the development of classic and modern algebraic geometry.
In this talk, I will recall how to use the geometry of (intermediate) Jacobians to obtain effective bounds on the size of automorphisms of the original variety. 
After presenting some fundamental results concerning the automorphism group of smooth hypersurfaces of the projective space, 
I will discuss some new results obtained in joint works (in progress) with Victor Gonzalez, Alvaro Liendo and Roberto Villaflor. These works were inspired by 
the classification groups which faithfully act on smooth cubic and quintic threefolds by Oguiso, Wei and Yu and by the work of Roulleau concerning 
the intermediate Jacobian of smooth cubic threefolds. If time allows us, I will discuss some open problems that arise from this.