Diane Davis

Advisor: Dr. Holger Kley

Degree Conferred: Summer 2007

After Graduation: Assistant Professor, Metro State College, Denver

Website: http://math.mscd.edu/metadot/index.pl

Thesis Title:

Toward a type Bn geometric Littlewood-Richardson rule

Abstract:

We 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 Math, volume 164).