The Bruhat order on Coxeter group is a partial orders of preeminent importance in wide parts of algebraic combinatorics, representation theory and algebraic geometry. While an active and lively research field, several problems in the area remain open, also in relation to Kazhdan-Lusztig polynomials and the celebrated Combinatorial Invariance Conjecture.

In this collaborative workshop will focus on the most recent developments on the Bruhat order, and, crucially, on open problems surrounding it. Our aim is to create new and advance existing collaborations on the subject of the workshop, and to substantially advance the state of the art.