Matthew Samuel's Math REU Project Page, 2007

Project: Enumerative Geometry, specifically, the computation of the equivariant structure constants of the Lagrangian Grassmannian

Update: Paper finished! Partial solution. Looking for journal.

Title: Equivariant Schubert calculus on isotropic Grassmannians
Abstract: We prove a partial rule for the equivariant Schubert calculus of the Lagrangian, odd orthogonal, and even orthogonal Grassmannians. Our proof is purely combinatorial. In the process, we derive new formulas for the restrictions of Schubert classes to fixed points of the torus action in these three Grassmannians, and give a bijective correspondence between shifted tableaux satisfying a compatibility condition and subwords of reduced words for minimal-length parabolic coset representatives that are themselves reduced words for minimal-length coset representatives in the Weyl groups.