Abstract: Pipe dreams and bumpless pipe dreams are two combinatorial objects that enumerate Schubert polynomials, and it has been an open problem to find a weight-preserving bijection between these two objects since bumpless pipe dreams were introduced by Lam, Lee and Shimozono. In this talk, we present such a bijection and establish its canonical nature by showing that it preserves Monk's rule. This is joint work with Daoji Huang.
