14:00-14:45 Matteo Tanzi

Ergodic Theory for High-Dimensional Systems: Expanding Maps Coupled in Networks

Abstract: TBC

15:00-15:45 Andrea Petracci

What is a scheme in algebraic geometry?

Abstract: Algebraic geometry is the study of loci defined by the vanishing of polynomial equations. After giving the definition of an affine algebraic variety and stating the celebrated Hilbert’s Nullstellensatz, I will motivate the necessity of more general objects than affine algebraic varieties: these will be schemes introduced by Alexander Grothendieck in the 1050s. Without going into technicalities, I will try to show how, thanks to scheme theory, it is possible to geometrically interpret some phenomena in number theory.

The talk will be completely introductory and no knowledge of algebraic geometry is needed.