The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
In this thesis we review the methods for computation of cosmological correlations in the early universe known as the in-in formalism which are then applied to the problem of magnetogenesis from inflation. For this computation, a power-law single...
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles ω = {ω[subscript t]}[subscript t∊[0,1]] on a locally compact Hausdorff groupoid Ɠ induces an isomorphism of the...
Coherent states. Quantum field theory. Nonlinear theories.
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
Cosmic acceleration could be an effect of a ""dark energy"" fluid pervading the Universe. It could also be an indication that general relativity is not the correct theory of gravity at cosmological length scales. Unfortunately, observations of the...
This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...
Psychopaths. Personality and emotions. Emotions and cognition.
Research investigating clinical and criminal psychopaths is quite extensive. Though it has evolved in terminology over the years, the basic premise and description of psychopathy has maintained deficits associated with emotional interpretation and...
As the ubiquitous complexity of common disease has become apparent, so has the need for novel tools and strategies that can accommodate complex patterns of association. In particular, the analytic challenges posed by the phenomena known as...
In this thesis, the dynamics of long-lived, time-dependent, coherent field configurations, known as oscillons, are investigated in the presence of an expanding background. In a (1+1)-dimensional expanding spacetime, scalar-field oscillon lifetimes...