Speaker:  Yibo Gao  (University of Michigan)

Title:  Quantum Bruhat graph and tilted Richardson varieties

Abstract: 

The quantum Bruhat graph is introduced by Postnikov to study structure constants of the quantum cohomology ring of the flag variety, with very rich combinatorial structures. We provide an explicit formula for the weight of minimal paths between any pair of permutations.  Building upon that, we obtain a simple criterion for the tilted Bruhat order studied by Brenti-Fomin-Postnikov. These results motivate the definition of tilted Richardson varieties, which provides geometrical interpretations of tilted Bruhat orders. Tilted Richardson varieties are indexed by pairs of permutations and generalize Richardson varieties in the flag variety. This is a joint work with Jiyang Gao and Shiliang Gao.