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Open Access Dissertation
Doctor of Philosophy (PhD)
Year Degree Awarded
Algebra | Discrete Mathematics and Combinatorics
The field of Schubert Calculus deals with computations in the cohomology rings of certain algebraic varieties, including flag varieties and Schubert varieties. In the equivariant setting, GKM theory turns multiplication in the cohomology ring of certain varieties into a combinatorial computation. This dissertation uses combinatorial tools, including Billey’s formula, to do Schubert calculus computations in several varieties. First we address do computations in the equivariant cohomology of full and partial flag varieties, the classical spaces in Schubert calculus. We then do computations in the equivariant cohomology of a family of non-classical spaces: regular nilpotent Hessenberg varieties. The final chapter gives a complete presentation for the cohomology ring of the Peterson variety, a type of regular nilpotent Hessenberg variety.
Drellich, Elizabeth J., "Combinatorics of Equivariant Cohomology: Flags and Regular Nilpotent Hessenberg Varieties" (2015). Doctoral Dissertations. 290.