Browsing Mathematics by Title
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Stationary distribution for spinning reflecting diffusions
(20120913)This dissertation studies two different types of interaction of diffusion processes with the boundary of a domain $DsubRR^n$, which is assumed to be bounded, and of class $C^2(RR^n)$. The first process that is studied is ... 
Strichartz estimates for wave equations with coefficients of Sobolev regularity
(2005)Wave packet techniques provide an effective method for proving Strichartz estimates on solutions to wave equations whose coefficients are not smooth. In this work, such methods are used to show Strichartz inequalities for ... 
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 ... 
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 ... 
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, ... 
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 ...