Browsing Mathematics by Title
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A TensorTriangulated Approach to Derived Categories of NonNoetherian Rings
(20120913)We investigate the subcategories and Bousfield lattices of derived categories of general commutative rings, extending previous work done under a Noetherian hypothesis. Maps between rings R → S induce adjoint functors between ... 
The geometry of uniform measures
Uniform measures have played a fundamental role in geometric measure theory since they naturally appear as tangent objects. They were first studied in the groundbreaking work of Preiss where he proved that a Radon measure ... 
The Inverse Problem of Thermoacoustic Tomography in Attenuating Media
Thermoacoustic tomography is a developing medical imaging technique that combines the propagation of electromagnetic and ultrasound waves with the purpose of producing a high contrast and high resolution internal image of ... 
Thermoacoustic Tomography in Elastic Media
(20131114)We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, nonhomogeneous elastic wave equation, given measurements of u on [0, T ] × boundary of Omega, where Omega in R3 ... 
Three Problems in Discrete Probability
In this thesis we present three problems. The first problem is to find a good description of the number of fixed points of a 231avoiding permutation. We use a bijection from Dyck paths to 231avoiding permutations that ... 
Timelike graphical models
We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical ... 
Topics in Continuum Theory
Continuum Theory is the study of compact, connected, metric spaces. These spaces arise naturally in the study of topological groups, compact manifolds, and in particular the topology and dynamics of onedimensional and ... 
The topology of graph homomorphisms
(2007)In this thesis we consider topological aspects of graph homomorphisms. Our main object of study is the Hom complex of graphs, a space first introduced by Lovasz to obtain lower bounds on chromatic number, and more recently ... 
Toward the compactification of the stack of Lie(G)forms using perfect complexes
To establish geometric properties of an algebraic stack, one can find a compactification. This method has been successfully employed to find irreducible components for example of the moduli stack of curves [DM69], vector ... 
Towards a nonQGorenstein Minimal Model Program
In this thesis we do the first steps towards a nonQGorenstein Minimal Model Program. We extensively study nonQfactorial singularities, using the techniques introduced by [dFH09]. We introduce a new class of singularities, ... 
Twistor Spaces for Supersingular K3 Surfaces
We develop a theory of twistor spaces for supersingular K3 surfaces, extending Artin's analogy between supersingular K3 surfaces and complex analytic K3 surfaces. Our twistor spaces are families of twisted supersingular ... 
Two Inverse Problems Arising in Medical Imaging
In this thesis, we discuss two inverse problems arising in medical imaging. The first problem is about a hybrid imaging method using coupled boundary measurements, which combines electrical impedance tomography (EIT) with ... 
Wild Automorphisms and Abelian Varieties
(2010)An automorphism $\sigma$ of a projective variety $X$ is said to be \textit{wild} if $\sigma(Y)\neq Y$ for every nonempty subvariety $Y\subsetneq X$. In MR2227726 Z. Reichstein, D. Rogalski, and J.J. Zhang conjectured that ... 
The Zeros of Elliptic Curve Lfunctions: Analytic Algorithms with Explicit Time Complexity
Elliptic curves are central objects of study in modernday algebraic number theory. The problem of how to determine the rank of a rational elliptic curve is a difficult one, and at the time of the writing of this thesis ...