Date of Award

5-2010

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Shasikant B. Mulay

Committee Members

David Anderson, Pavlos Tzermias, Michael Langston

Abstract

This thesis discusses intersections of the Schubert varieties in the flag variety associated to a vector space of dimension n. The Schubert number is the number of irreducible components of an intersection of Schubert varieties. Our main result gives the lower bound on the maximum of Schubert numbers. This lower bound varies quadratically with n. The known lower bound varied only linearly with n. We also establish a few technical results of independent interest in the combinatorics of strong Bruhat orders.

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