Now showing items 21-40 of 81

• #### Equivariant Weiss Calculus and Loops of Stiefel Manifolds ﻿

(2016-05-18)
In the mid 1980s, Steve Mitchell and Bill Richter produced a filtration of the Stiefel manifolds O(V ;W) and U(V ;W) of orthogonal and unitary, respectively, maps V -> V ⊕W stably split as a wedge sum of Thom spaces defined ...
• #### A Formula for Some Shalika Germs ﻿

(2015-05-17)
In this article, for nilpotent orbits in (the Lie algebras of) ramified quasi-split unitary groups with two Jordan blocks, we give the values of their Shalika germs at certain equi-valued elements with half-integral depth ...
• #### Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case ﻿

(2016-05-13)
In this thesis, we study finite locally free group schemes, Galois deformation rings, and Barsotti-Tate representations in the relative case. We show three independent but related results, assuming p > 2. First, we give ...
• #### 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 ...
• #### 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 ...
• #### The Geometry of Hurwitz Space ﻿

(2013-09-30)
We explore the geometry of certain special subvarieties of spaces of branched covers which we call the Maroni and Casnati-Ekedahl loci. Our goal is to understand the divisor theory on compactifications of Hurwitz space, ...
• #### The Geometry of the Weil-Petersson Metric in Complex Dynamics ﻿

(2014-06-06)
In this work, we study an analogue of the Weil-Petersson metric on the space of Blaschke products of degree 2 proposed by McMullen. We show that the Weil-Petersson metric is incomplete and study its metric completion. Our ...
• #### Goodwillie Approximations to Higher Categories ﻿

(2015-05-14)
Goodwillie calculus involves the approximation of functors between higher categories by so-called polynomial functors. We show (under mild hypotheses) how to associate to a higher category C a Goodwillie tower, consisting ...
• #### Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications ﻿

(2013-10-08)
Suppose $f,g_1,\cdots,g_p$ are holomorphic functions over $\Omega\subset\cxC^n$. Then there raises a natural question: when can we find holomorphic functions $h_1,\cdots,h_p$ such that $f=\sum g_jh_j$? The celebrated Skoda ...
• #### Indirect Reciprocity With Optional Interactions and Private Information and Stochastic Evolution of Staying Together ﻿

(2019-04-17)
We explore indirect reciprocity with optional interactions and private information and stochastic evolution of staying together. Indirect reciprocity is cooperation based on reputation in a group of players; my behavior ...
• #### Integral canonical models for G-bundles on Shimura varieties of abelian type ﻿

(2017-05-02)
This thesis builds on Kisin's theories of S-modules and integral models for Shimura varieties of abelian type to further our understanding of the arithmetic of Shimura varieties in several directions. First, we show that ...
• #### Interpolation and Vector Bundles on Curves ﻿

(2015-05-05)
Interpolation is a property of vector bundles on curves closely related to slope stability. The notion is motivated by the deformation theory of curves in projective space incident to given fixed subvarieties. If the normal ...
• #### 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 ...
• #### Local-Global Compatibility and the Action of Monodromy on nearby Cycles ﻿

(2012-12-19)
In this thesis, we study the compatibility between local and global Langlands correspondences for $GL_n$. This generalizes the compatibility between local and global class field theory and is related to deep conjectures ...
• #### Mapping Class Groups, Homology and Finite Covers of Surfaces ﻿

(2012-12-20)
Let S be an orientable surface of genus g with n punctures, such that $\chi(S) = 2 − 2g − n < 0$. Let $\psi \epsilon Mod(S)$ denote an element in its mapping class group. In this thesis, we study the action of $\psi$ ...
• #### Mathematical Models of Cancer ﻿

(2013-02-22)
Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major ...
• #### Mirror Symmetry, Autoequivalences, and Bridgeland Stability Conditions ﻿

(2019-05-03)
The present thesis studies various aspects of Calabi-Yau manifolds, including mirror symmetry, systolic geometry, and dynamical systems. We construct the mirror operation of Atiyah flop in symplectic geometry. We construct ...
• #### The mod 2 homology of free spectral Lie algebras ﻿

(2015-05-14)
The Goodwillie derivatives of the identity functor on pointed spaces form an operad ∂(Id) in spectra. We compute the mod 2 homology of free algebras for this operad on suspension spectra of simply-connected spaces.
• #### 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 ...
• #### Modularity of some elliptic curves over totally real fields ﻿

(2014-06-06)
In this thesis, we investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular j-invariants. By analyzing quadratic points on some modular ...