Bijective combinatorics in Schubert calculus with pipe dreams and bumpless pipe dreamsAlgebra & Discrete Mathematics
|Speaker:||Daoji Huang, University of Minnesota, Twin Cities|
|Start time:||Mon, Nov 8 2021, 11:00AM|
Pipe dreams and bumpless pipe dreams both give combinatorial formulas for Schubert polynomials. As a result, many important identities in Schubert calculus can be understood through pipe dreams and/or bumpless pipe dreams. Since the discovery of bumpless pipe dreams, a direct weight-preserving bijection between pipe dreams and bumpless pipe dreams has been of great interest. In this talk, we present such a bijection, and establish its canonical nature by showing that it preserves Monk's rule. We also remark that the technical recipe used in this bijection has been useful in a few other contexts, including a combinatorial rule for Schubert structure constants in the separated descent Schubert problem. The work on the canonical bijection is joint with Yibo Gao.