Mathematics

I will split this seminar in two parts. In the first part I will introduce the needed instrument in order to state Green conjecture. This part will be more foundational and it will be mostly about curves. In particular I will introduce the notions of gonality and Clifford index and I will show how, the latter, is related to the complexity of a canonical curve. This complexity will be encoded by the Koszul cohomology, an algebraic tool introduced, in the geometry context, by Mark Green in '84.In the second part I will give an idea on how Claire Voisin solved the conjecture by involving K3 surfaces. The first part will be one hour long then we will take a small break for the questions and then resume with the second part which will last half an hour and it will be more technical.