Correlation Inequalities for Schur Functions and Young Tableaux

Explore correlation inequalities for Schur functions and Young tableaux in this 50-minute lecture presented by Igor Pak from the University of California, Los Angeles. Delivered at IPAM's Integrability and Algebraic Combinatorics Workshop, the talk provides an overview of both established results and recent developments in the field. Delve into the explosion of correlation inequalities in recent decades, including the well-known FKG inequality, and their applications in Probability, Statistical Physics, matroid inequalities, Algebraic Combinatorics, and Poset Theory. Examine older findings such as Fishburn and Björner inequalities, Lam-Postnikov-Pylyavskyy inequalities, and discover new insights from Pak's joint work with Swee Hong Chan and Greta Panova. Gain a deeper understanding of this rapidly evolving area of mathematics and its interdisciplinary connections.