Now showing items 4-23 of 96

    • Boundary Harnack Principle for Stable-Like Processes 

      Rudnick, Christian
      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 

      Lou, Shuwen
      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 ...
    • The C*-algebra of a finite T_0 topological space 

      McMurdie, Christopher Robert
      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 ...
    • Classification of connected Hopf algebras up to prime-cube dimension 

      Wang, Xingting
      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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • Dual Equivalence Graphs and their Applications 

      Roberts, Austin
      In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's ...
    • Eigenvalue fluctuations for random regular graphs 

      Johnson, Tobias Lee
      One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are <italic>universal</italic>. We probe the edges of universality by studying ...
    • Eigenvalue Fluctuations of Random Matrices beyond the Gaussian Universality Class 

      Paquette, Elliot (2013-11-14)
      The goal of this thesis is to develop one of the threads of what is known in random matrix theory as universality, which essentially is that a large class of matrices generalizing the Gaussian matrices (certain Wigner ...
    • An electrodynamic inverse problem in chiral media 

      McDowall, Stephen R., 1969- (1998)
      We consider the inverse problem of determining the electromagnetic material parameters of a body from information obtainable only at the boundary of the body; such information comes in the form of a boundary map which we ...
    • Elliptic Inverse Problems 

      Yang, Yang
      Inverse problems arise in various areas of science and engineering including medical imaging, computer vision, geophysics, solid mechanics, astronomy, and so forth. A wide range of these problems involve elliptic operators. ...