Explore the recent advances in Hodge theory of complex algebraic varieties in this 42-minute lecture by Bruno Klingler. Delve into the transcendental comparison of two algebraic structures and learn how o-minimal geometry is used to bound this transcendence. Examine topics such as Hodge theory in families, Hodge classes, general topology, and intersection theory. Discover the applications of these concepts in biology and arithmetic aspects. Access the accompanying slides for a comprehensive understanding of this complex mathematical subject.