Back-to-School Seminar: Pipe dreams and Rubey’s lattice

Reduced pipe dreams are combinatorial objects that encode some of the algebraic, enumerative, geometric, and probabilistic properties of Schubert and Grothendieck polynomials. In this talk, we will introduce the basic properties of pipe dreams and the Rubey poset on reduced pipe dreams. We will then discuss the two recent papers by Axelrod-Freed, Defant, Mularczyk, Nguyen, Tung and Billey, Minnerath, McCausland which independently proved that the Rubey poset is a lattice.