The past decades has seen some spectacular achievements on the ineraction beetween representation theory of groups or algebras of Lie type and models coming from probability or theoritical physics, cementing its reputation as a highly active area involving mathematicians from across the world. This workshop not only aims to present some of these new results, but also to explore new domains in connection with the PRC Cortipom project granted by the Agence National de la Recherche. It will feature talks given by confirmed researchers and also more informal presentations and works in small groups.