Birational Geometry of Hypersurfaces: Gargnano del Garda, Italy, 2018

- Part I Birational Invariants and (Stable) Rationality. - Birational Invariants and Decomposition of the Diagonal. - Non rationalité stable sur les corps quelconques. - Introduction to work of Hassett-Pirutka-Tschinkel and Schreieder. - Part II Hypersurfaces. - The Rigidity Theorem of Fano-Segre-Iskovskikh-Manin-Pukhlikov-Corti-Cheltsov-deFernex-Ein-Mustaţă-Zhuang. - Hodge Theory of Cubic Fourfolds, Their Fano Varieties, and Associated K3 Categories. - Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces. - Appendix: Introduction to Derived Categories of Coherent Sheaves.