On the Irrationality of Intersections of Quadrics

In this 55-minute lecture, explore the continuing influence of Lefschetz's century-old ideas on modern geometry as Professor Ron Donagi from the University of Pennsylvania discusses the irrationality of intersections of quadrics. Survey key rationality and irrationality results in algebraic geometry and their relationship to non-commutative spaces. Learn how the natural non-commutative space attached to an intersection of three quadrics in P7 is truly non-commutative, and discover how the new theory of Hodge atoms proves that a very general intersection of three quadrics in P7 is not rational. The presentation covers joint work with Tony Pantev, offering valuable insights into contemporary geometric research.