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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
We investigate some algebro-geometric aspects of several families of elliptic fibrations relevant for F-theory model building along with some physical applications. In particular, we compute topological invariants of elliptic fibrations...
This dissertation finds some partial results in support of two positivity conjectures regarding the Chern-Schwartz-MacPherson (CSM) classes of graph hypersurfaces (conjectured by Aluffi and Marcolli) and Schubert varieties (conjectured...
This thesis carefully reviews computational methods that will act as a tool in the research of Riemann surfaces. We are interested in representing a Riemann surface from many equivalent points of view. The goal is to define a Riemann...
The Shafarevich-Tate group of an elliptic curve is an important invariant of the curve whose conjectural finiteness can sometimes be used to determine the rank of the curve. The second part of the Birch and Swinnerton-Dyer (BSD)...
This thesis consists of three independent projects in the field of algebraic geometry. The first of these is the focus of Chapter 2. There we define a family of integer sequences we refer to as the family of secant indices of projective...
In this thesis we generalize results from classical Coxeter systems to mixed-sign Coxeter systems which are denoted by a triple (W, S, B)consisting of a reflection group W, a distinguished set of generators Sfor the group for W, and a...
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