Davis, Diane E., authorKley, Holger, advisor2024-03-132024-03-132007https://hdl.handle.net/10217/237673We conjecture a geometric Littlewood-Richardson Rule for the maximal orthogonal Grassmannian and make significant advances in the proof of this conjecture. We consider Schubert calculus in the presence of a nondegenerate symmetric bilinear form on an odd-dimensional vector space (the type Bn setting) and use degenerations to understand intersections of Schubert varieties in the odd orthogonal Grassmannian. We describe the degenerations using combinatorial objects called checker games. This work is closely related to Vakil's Geometric Littlewood-Richardson Rule (Annals of Mathematics, 164).born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.algebraic geometrychecker gamesdegenerationsGrassmannianLittlewood-Richardson RuleSchubert calculusvector spacesmathematicsTextPer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.