Date of Graduation

12-2022

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Lance E. Miller

Committee Member

Paolo Mantero

Second Committee Member

Justin Lyle

Keywords

Bass Numbers, Clique Graphs, Edge Ideals, Local Cohomology, Lyubeznik Numbers

Abstract

Lyubeznik numbers, defined in terms of local cohomology, are invariants of local rings that are able to detect many algebraic and geometric properties. Notably they recognize topological behaviors of various structures associated to their rings. We will discuss computations of these numbers for unmixed edge ideals by giving a completely combinatorial construction which realizes the connectedness information captured by these numbers.

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