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Bijective combinatorics in Schubert calculus with pipe dreams and bumpless pipe dreams

Algebra & Discrete Mathematics

Speaker: Daoji Huang, University of Minnesota, Twin Cities
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Location: Zoom
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.