Title: Area considerations in Real Algebraic Geometry

Abstract: These lectures are devoted to real algebraic curves in real algebraic surfaces and to areas delimited by these curves. We will start with several basic notions and facts in topology of real algebraic curves and surfaces paying a particular attention to algebraic curves in the real plane. The discussion around amoebas and areas of these curves will naturally lead us to the notion of simple Harnack curves. After the study of various properties of simple Harnack curves, we will present analogs of these curves in the framework of K3-surfaces and will finish the lectures by introducing areas of connected components of the real point set of a real K3-surface (using a holomorphic symplectic form of the surface) and establishing certain inequalities for these areas.

Lecture 2. Wednesday, October 20 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

Topology of real algebraic curves and surfaces by Ilia Itenberg.