Discrete and Continuous Duality Algebras

Explore the intricacies of discrete and continuous duality algebras in this advanced mathematics lecture. Delve into classical constructions associating Poincare duality algebras with homogeneous polynomials on vector spaces, and their applications in presenting cohomology rings of complete smooth toric varieties and spherical varieties. Examine two recent generalizations of duality algebra construction: one involving weighted homogeneous polynomials, enabling the creation of Poincare duality algebras not necessarily generated in degree 1, and a discrete analogue associating Gorenstein duality algebras with polynomials on lattices. Gain insights into the implications of these extensions, including presentations for K-rings of smooth complete toric varieties and full flag varieties. This talk, delivered by Leonid Monin from École Polytechnique Fédérale de Lausanne, offers a deep dive into advanced algebraic concepts for mathematics enthusiasts and researchers.