Notes on Macdonald polynomials and the geometry of Hilbert schemes -- The Laplacian method -- Kerov’s central limit theorem for the Plancherel measure on Young diagrams -- Symmetric functions and the Fock space -- An introduction to birational Weyl group actions -- Symmetric functions and random partitions -- Prom Littlewood-Richardson coefficients to cluster algebras in three lectures.
Summary
This book surveys recent developments and outlines research prospects in various fields, the fundamental questions of which can be stated in the language of symmetric functions. Interdisciplinary interconnections are emphasized.