Browsing Mathematics by Title
Now showing items 17-36 of 188
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Bin packing, number balancing, and rescaling linear programs
This thesis deals with several important algorithmic questions using techniques from diverse areas including discrepancy theory, machine learning and lattice theory. In Chapter 2, we construct an improved approximation ... -
Birational Functors in the Derived Category
In this thesis, we study a class of derived equivalences that naturally induce birational maps. We give several equivalent criteria for a birational correspondence to exist, and prove the correspondence induces a $K$-equivalece, ... -
Bispectral Operator Algebras
This dissertation is an amalgamation of various results on the structure of bispectral differential operator algebras, ie. algebras of differential operators with possibly noncommutative coefficients in a variable $x$ ... -
Boundary Harnack Principle for Stable-Like Processes
We establish the boundary Harnack principle for certain classes of symmetric stable-like processes in $\mathbf{R}^d$ on arbitrary open sets as well as censored stable-like processes on $\mathcal{C}^{1,1}$-domains. Using ... -
Brownian Motion on Spaces with Varying Dimension
In this thesis we introduce and study Brownian motion with or without drift on state spaces with varying dimension. Starting with a concrete such state space that is the plane with an infinite pole on it, we construct a ... -
Brownian Motion, Quasiconformal Mappings and the Beltrami Equation
Consider a Jordan domain $\Omega$ in the plane with $3$ distinct points marked on its boundary. These $3$ points split $\partial \Omega$ into $3$ arcs. For each $z \in \Omega$, we can assign it the harmonic coordinates by ... -
Brownian particles interacting with a Newtonian Barrier: Skorohod maps and their use in solving a PDE with free boundary, strong approximation, and hydrodynamic limits.
In this thesis, we pioneer the use of Skorohod maps in establishing the hydrodynamic behavior of an interacting particle system. This technique has the benefit of using stochastic methods to show both existence and uniqueness ... -
The C*-algebra of a finite T_0 topological space
We are concerned with the following motivating question: how can one extend the classical Gelfand-Naimark theorem to the simplest non-Hausdorff topological spaces? Our model space is a finite $T_0$ topological space, or ... -
Chirality in Multiview Geometry
This thesis studies mathematical problems associated with reconstructing a three dimensional scene from images. Using the traditional pinhole camera model and tools from multiview geometry, we pose these problems from an ... -
Classification of connected Hopf algebras up to prime-cube dimension
We classify all connected Hopf algebras up to p^3 dimension over an algebraically closed field of characteristic p>0 under the mild restriction such that in dimension p^3, we only work over odd primes p when the primitive ... -
Classification of Line Modules and Finite Dimensional Simple Modules over a Deformation of the Polynomial Ring in Three Variables
Let $\Bbbk$ be a field and $A$ the non-commutative $\Bbbk$-algebra generated by $x_1, x_2, x_3$ subject to the relations $$ q x_ix_j - q^{-1} x_jx_i \; = \; x_k $$ as $(i,j,k)$ ranges over all cyclic permutations of ... -
Combinatorial Laguerre Series
(2014-02-24)We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials. We describe how such a series can be computed by ... -
Combinatorics and Representation Theory of Rank Varieties, Springer Fibers, and Hyperplane Arrangements
This thesis is dedicated to applications of symmetric function theory to problems in combinatorics, representation theory, and geometry. Crucial to our applications is the Frobenius characteristic map from Algebraic ... -
Combinatorics of CAT(0) cubical complexes, crossing complexes and co-skeletons
This thesis consists of three papers about cubical complexes: Chapter 1 is [Rowlands 22a], Chapter 2 is [Rowlands 23], and Chapter 3 is [Rowlands 22b]. Chapter 1 extends a result by Dancis to cubical complexes: Dancis ... -
Compact Moduli of Surfaces in Three-Dimensional Projective Space
The main goal of this paper is to construct a compactification of the moduli space of degree $d \ge 5$ hypersurfaces in $\mathbb{P}^3$, i.e. a parameter space whose interior points correspond to (equivalence classes of) ... -
Competing Brownian Particles
Consider a finite system of N Brownian particles on the real line. Rank them from bottom to top: the (currently) lowest particle has rank 1, the second lowest has rank 2, etc., up to the top particle, which has rank N. The ... -
Computational aspects of modular parametrizations of elliptic curves
\abstract{ We investigate computational problems related to modular parametrizations of elliptic curves defined over $\mathbb{Q}$. We develop algorithms to compute the Mazur Swinnerton-Dyer critical subgroup of elliptic ... -
Computations Related to the Construction of Finite Genus Solutions to the Kadomtsev-Petviashvili Equation
Krichever's method of integrating certain partial differential equations using algebro-geometric techniques provides an explicit approach to the construction of finite-genus solutions to the Kadomtsev-Petviashvili (KP) ... -
Conformal Welding of Dendrites
We investigate the conformal welding problem, which is a way of taking quotients of Riemann surfaces by identifying points on their boundaries. The existence and uniqueness of this operation is in general difficult to ... -
Conformal welding of uniform random trees
A conformally balanced tree is an embedding of a given planar map into the plane with constraints on the harmonic measure of its edges such that the resulting set is unique up to scale and rotation. Bishop (2013) showed ...