Homological Algebraic Geometry

Explore the fascinating world of homological algebraic geometry in this one-hour lecture by Alexander Kuznetsov, presented at the International Mathematical Union. Delve into the study of algebraic variety geometry through the structure of its derived category of coherent sheaves, a concept pioneered by Bondal and Orlov at the turn of the millennium. Discover the central concept of semiorthogonal decomposition and its rapidly developing story. Examine three key aspects: semiorthogonal components with interesting properties and their geometric significance, categorical extensions of classical geometric constructions (including homological projective duality, categorical joins and cones, and categorical resolutions of singularities), and innovative constructions such as categorical absorptions of singularities. Access the accompanying presentation slides for a visual aid to enhance your understanding of this complex mathematical topic.