Recorded 19 April 2024. Houcine Ben Dali of the Université de Lorraine presents "Jack characters as generating series of bipartite maps and proof of Lassalle’s conjecture" at IPAM's Integrability and Algebraic Combinatorics Workshop. Abstract: Representation theory of the symmetric group allows to connect Schur symmetric functions to generating series of maps on orientable surfaces. Several conjectures suggest that Jack polynomials, a one parameter deformation of Schur functions, are related to the enumeration of non-orientable maps counted with a "non-orientability" weight. In this talk, I present an explicit formula for the power-sum expansion of Jack polynomials. This formula allows to prove a conjecture of Lassalle from 2008 on integrality and positivity of Jack characters in Stanley’s coordinates. This talk is based on a joint work with Maciej Dolega. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-integrability-and-algebraic-combinatorics/