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Several problems on moduli stacks of hyperelliptic curves
(University of Missouri--Columbia, 2023)
The main objects to investigate in this thesis are the moduli stacks of smooth hyperelliptic curves of genus g, denoted by Hg, and its Deligne-Mumford compactification Hg in Mg. A result by Kleiman and Lonsted says that ...
Relative subrepresentation theorem for a finite central extension of a reductive group
(University of Missouri--Columbia, 2023)
Jacquet's subrepresentation theorem asserts that any irreducible admissible representation of a reductive p-adic group is a subrepresentation of IndG P ([tau]), where P is a parabolic subgroup of G and [tau] is a cuspidal ...
Stochastic forms of functional isoperimetric inequalities
(University of Missouri--Columbia, 2021)
The Brunn-Minkowski and Prekopa-Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions, so it seems that ...
Absolute continuity of parabolic measure and the initial-dirichlet problem
(University of Missouri--Columbia, 2019)
This thesis is devoted to the study of parabolic measure corresponding to a divergence form parabolic operator. We first extend to the parabolic setting a number of basic results that are well known in the elliptic case. ...
Structural features of persistent homology and their algorithmic transformations
(University of Missouri--Columbia, 2021)
We re-examine the theory and orthodox methods that underlie the study of persistent homology, particularly in its calculation of homological cycle representatives that are associated to persistence diagrams. A common ...
Volumes of line bundles on schemes
(University of Missouri--Columbia, 2021)
The volume of a line bundle is an invariant defined in terms of a limit superior. It is a fundamental question whether this limit superior is a limit. It has been shown that this is always the case on generically reduced ...
Random sections of star bodies
(University of Missouri--Columbia, 2023)
This thesis concerns analytic and geometric aspects of random sections of star bodies and their implications for problems in stochastic geometry. We treat isoperimetric inequalities and distribution of volumes of such ...
A Quiver Invariant theoretic approach to radial isotropy and the Paulsen problem for matrix frames
(University of Missouri--Columbia, 2022)
In this dissertation, we view matrix frames as representations of quivers and study them within the general framework of Quiver Invariant Theory. We are particularly interested in radial isotropic and Parseval matrix frames. ...
The asymptotic Samuel function of a filtration
(University of Missouri--Columbia, 2023)
We extend the asymptotic Samuel function of an ideal to an arbitrary filtration of a Noetherian ring. We observe that although many properties that hold true in the ideal case are true for filtrations, there are many ...
On toric varieties and toric stacks
(University of Missouri--Columbia, 2023)
In this dissertation, we prove a number of results about toric varieties by utilizing Cox's construction of a toric variety as a good quotient of an open subset of affine space by the action of a diagonalizable group. Our ...
Capillary-gravity water waves with vorticity : steady wind-driven waves and waves with a submerged dipole
(University of Missouri--Columbia, 2019)
In this thesis, we study two mathematical problems on water waves in the setting of the incompressible Euler equations with vorticity, gravity, and surface tension. We investigate the existence of small-amplitude steady ...
Complex and almost-complex structures on six dimensional manifolds
(University of Missouri--Columbia, 2006)
We investigate the properties of hypothetical exotic complex structures on three dimensional complex projective space CP³. This is motivated by the long standing question in differential geometry of whether or not the six ...
Directional time-frequency analysis with applications
(University of Missouri--Columbia, 2006)
The purpose of this dissertation is to introduce a new directionally-sensitive time frequency representation of a function. It is shown that we may break up a function (or signal) into individual time-frequency-direction ...
Stability estimates for semigroups and partly parabolic reaction diffusion equations
(University of Missouri--Columbia, 2013)
The purpose of my dissertation is the application of the methods of abstract theory of strongly continuous operator semigroups (and of evolution semigroups in particular) to study of the spectral properties of a class of ...
Age-dependent branching processes and applications to the Luria-Delbrck experiment
(University of Missouri--Columbia, 2015)
Microbial populations adapt to their environment by acquiring advantageous mutations, but in the early twentieth century, questions about how these organisms acquire mutations arose. The experiment of Salvador Luria and ...
Frames and applications : distribution of frame coeficients, integer frames and phase retrieval
(University of Missouri--Columbia, 2015)
The present dissertation is divided into two main areas: frame theoretic results and applications of frames. In particular, the beginning half develops the first detailed theory of the distribution of frame coefficients. ...
On projective morphisms of varieties with nef anticanonical divisor
(University of Missouri--Columbia, 2012)
We shall study and discuss some important properties of the projective varieties with nef anticanonical bundles and nef tangent bundles. And we shall review some background and history about the subject. Then we shall use ...
Frames and projections
(University of Missouri--Columbia, 2013)
In this dissertation we explore several ways in which the concept of projections arise infinite frame theory. In the first chapter we show that the Paulsen problem from frame theory is equivalent to a long standing open ...
Generating sequences of valuations and applications
(University of Missouri--Columbia, 2014)
Irrational behavior of algebraic discrete valuationsIrrational behavior of algebraic discrete valuations
(University of Missouri--Columbia, 2014)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] We construct a family of algebraic discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasi-polynomial and ...