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Arithmetic properties and decomposability of Jacobians
(Massachusetts Institute of Technology, 2018)
We first give an overview of methods used to study the decomposability of Jacobians of curves over the complex numbers. This involves studying the action of a finite group on an abelian variety in general. Next, we use ...
List coloring in general graphs
(Massachusetts Institute of Technology, 2015)
In this thesis we explore some of the relatively new approaches to the problem of list-coloring graphs. This is a problem that has its roots in classical graph theory, but has developed an entire theory of its own, that ...