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Entire Surfaces of Prescribed Curvature in Minkowski 3-Space
(2018-05-16)
This thesis concerns the global theory of properly embedded spacelike surfaces in 3 dimensional Minkowski space with prescribed Gaussian curvature. We prove that every regular domain which is not a wedge contains a unique ...
Variations on a Nilpotence Theorem of Hopkins and Mahowald
(2018-05-08)
It is a theorem of Hopkins and Mahowald that the nilpotence of $p$-torsion classes in $\mathbb{E}_2$-ring spectra can be detected by the classical $H\mathbb{F}_p$-Hurewicz homomorphism. On the other hand, the May Nilpotence ...
Some Calculations of Cobordism Groups and Their Applications in Physics
(2018-05-11)
In this paper, we compute several cobordism groups. We use these calculations to classify invertible extended topological field theory with Hn structures and give a classification of Symmetric Protected Topological (SPT) ...
Nearby Cycles of Whittaker Sheaves
(2018-05-13)
In this thesis we study the nearby cycles of a Whittaker sheaf as it degenerates to an object of the principal series category. In the case of a finite-dimensional flag variety, we prove that the nearby cycles sheaf ...
Geometric Variational Problems for Mean Curvature
(2018-05-01)
This thesis investigates variational problems related to the concept of mean curvature on submanifolds. Our primary focus is on the area functional, whose critical points are the minimal submanifolds and whose gradient ...
Teichmüller Curves in Genus Two: Square-Tiled Surfaces and Modular Curves
(2018-05-13)
This work is a contribution to the classification of Teichm\"uller curves in the moduli space $\M_2$ of Riemann surfaces of genus 2. While the classification of primitive Teichm\"uller curves in $\M_2$ is complete, the ...
Local Statistics of Dyson Brownian Motion
(2018-04-26)
The time to equilibrium of the local statistics of Dyson Brownian motion with general initial data is investigated. In the bulk of the spectrum it is established that the local statistics coincide with the invariant GOE/GUE ...
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 ...