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Mod-P Isogeny Classes on Shimura Varieties With Parahoric Level Structure
(2017-05-11)
We study the special fiber of the integral models for Shimura varieties of Hodge type with parahoric level structure constructed by Kisin and Pappas in \cite{KP}. We show that when the group is residually split, the points ...
Picard-Fuchs Systems Arising From Toric and Flag Varieties
(2018-05-12)
This thesis studies the Picard-Fuchs systems for families arising as vector bundles zero loci in toric or partial flag varieties, including Riemann-Hilbert type theorems and arith- metic properties of the differential ...
Universality of Random Matrices With Dependent Entries
(2018-05-11)
This dissertation deals with two random matrix models with dependent entries. The first model is a random matrix with generic slow-varying correlation. The second model is the addition of two Hermitian matrices, conjugated ...
Geometric Properties of Families of Galois Representations
(2018-05-10)
This thesis concerns families of Galois representations arising as etale local systems on a variety over a number field or a p-adic field.
The first part of the thesis studies families of Galois representations of number ...
Several Compactness Results in Gauge Theory and Low Dimensional Topology
(2018-05-13)
This thesis studies several compactness problems in gauge theory and explores their applications is low dimensional topology.
The first chapter studies a connection between taut foliations and Seiberg-Witten theory. Let Y ...