Now showing items 28-47 of 188

    • Combinatorial Laguerre Series 

      Taylor, Jair Patrick (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 

      Griffin, Sean
      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 

      Rowlands, Rowan
      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 

      DeVleming, Kristin Elizabeth
      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 

      Sarantsev, Andrey
      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 

      Chen, Hao
      \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 

      Bennett, Mark Syd
      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 

      Lin, Peter
      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 

      Barnes, Joel
      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 ...
    • Connections Between Lanczos Iteration and Orthogonal Polynomials 

      Green, Christopher (2010-01-10)
      In this thesis we examine the connections between orthogonal polynomials and the Lanczos algorithm for tridiagonalizing a Hermitian matrix. The Lanczos algorithm provides an easy way to calculate and to estimate the ...
    • Convergence and approximation for primal-dual methods in large-scale optimization 

      Wright, Stephen E., 1962- (1990)
      Large-scale problems in convex optimization often can be reformulated in primal-dual (minimax) representations having special decomposition properties. Approximation of the resulting high-dimensional problems by restriction ...
    • Convex Optimization over Probability Measures 

      Jordan-Squire, Christopher
      The thesis studies convex optimization over the Banach space of regular Borel measures on a compact set. The focus is on problems where the variables are constrained to be probability measures. Applications include ...
    • Convexity, convergence and feedback in optimal control 

      Goebel, Rafal, 1971- (2000)
      The results of this thesis are oriented towards the study of convex problems of optimal control in the extended piecewise linear-quadratic format. Such format greatly extends the classical linear-quadratic regulator problem ...
    • Cornered Asymptotically Hyperbolic Metrics 

      McKeown, Stephen Edward
      This thesis considers asymptotically hyperbolic manifolds that have a finite boundary in addition to the usual infinite boundary – cornered asymptotically hyperbolic manifolds. A theorem of Cartan-Hadamard type near infinity ...
    • Counting social interactions for discrete subsets of the plane 

      Fairchild, Samantha Kay
      We will use dynamical, geometric, and analytic techniques to study translation surfaces. A translation surface is, informally, a collection of polygons in the plane with parallel sides identified by translation to form a ...
    • Cubes, Codes, and Graphical Designs 

      Babecki, Catherine
      Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical ...
    • Cycle type factorizations in the finite general linear groups 

      Gordon, Graham Walker
      Recent work by Huang, Lewis, Morales, Reiner, and Stanton suggests that the regular elliptic elements of $\mathrm{GL}_n \mathbb{F}_q$ are somehow analogous to the $n$-cycles of the symmetric group. In 1981, Stanley enumerated ...
    • Deformation invariance of rational pairs 

      Erickson, Lindsay
      Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the ...
    • Deformations of Categories of Coherent Sheaves and Fourier-Mukai Transforms 

      Grigg, Nathan (2013-07-25)
      In modern algebraic geometry, an algebraic variety is often studied by way of its category of coherent sheaves or derived category. Recent work by Toda has shown that infinitesimal deformations of the category of coherent ...
    • Designing Scheduling Algorithms via a Mathematical Perspective 

      Davies, Sami
      This document will discuss three problems that I worked on during my Ph.D. Chapter \ref{chapter: SC} contains my work on the Santa Claus problem, and Chapters \ref{chapter: S1} and \ref{chapter: S2} contain my work on ...