Now showing items 149-168 of 188

    • Self-shrinking Solutions to Mean Curvature Flow 

      Drugan, Gregory
      We construct new examples of self-shrinking solutions to mean curvature flow. We first construct an immersed and non-embedded sphere self-shrinker. This result verifies numerical evidence dating back to the 1980's and shows ...
    • Selmer groups for elliptic curves with isogenies of prime degree 

      Mailhot, James Michael (2003)
      The Mordell-Weil theorem states that the points of an elliptic curve defined over a number field form a finitely generated, abelian group. The rank of this group, generally referred to as the rank of the elliptic curve, ...
    • Sheaves on support varieties and varieties of elementary subalgebras 

      Stark, James
      We present several results about two closely related types of objects: the projectivized scheme $\PG$ of one parameter subgroups of an infinitesimal group scheme $G$ and the variety $\bE(\fg)$ of maximal elementary subalgebras ...
    • Shimura Degrees for Elliptic Curves over Number Fields 

      Deines, Alyson Laurene
      A crowning achievement of Number theory in the 20th century is a theorem of Wiles which states that for an elliptic curve E over <bold>Q</bold> of conductor N, there is a non-constant map from the modular curve of level N ...
    • Singular Moduli and the Ideal Class Group 

      Geiger, Caleb Laarz
      Let $d_1$ and $d_2$ be discriminants of distinct quadratic imaginary orders $\cO_{d_1}$ and $\cO_{d_2}$ and let $J(d_1,d_2)$ denote the product of differences of CM $j$-invariants with discriminants $d_1$ and $d_2$. In ...
    • Smoothness of Loewner Slits 

      Wong, Chun Wai Carto (2013-02-25)
      In this dissertation, we show that the chordal Loewner differential equation with C^{beta} driving function generates a C^{beta + 1/2} slit for 1/2 < beta <= 2, except when beta = 3/2 the slit is only proved to be weakly C^{1,1}.
    • Some cohomology of finite general linear groups 

      Sprehn, David
      We prove that the degree r(2p − 3) cohomology of any (untwisted) finite group of Lie type over F_(p^r), with coefficients in characteristic p, is nonzero as long as its Coxeter number is at most p. We do this by providing ...
    • Some Inverse Problems in Analysis and Geometry 

      ASSYLBEKOV, YERNAT
      The aim of a typical inverse problem is to recover the interior properties of a medium by making measurements only on the boundary. These types of problems are motivated by geophysics, medical imaging and quantum mechanics ...
    • Some Linear and Nonlinear Geometric Inverse Problems 

      Zhou, Hanming
      Inverse problems is an area at the interface of several disciplines and has become a prominent research topic due to its potential applications. A wide range of these problems can be formulated under various geometric ...
    • Some Theorems on the Resolution Property and the Brauer map 

      Mathur, Siddharth
      Using formal-local methods, we prove that a separated and normal Deligne-Mumford surface must satisfy the resolution property, this includes the first class of separated algebraic spaces which are not schemes. Our analysis ...
    • Spectral analysis in bipartite biregular graphs and community detection 

      Brito, Gerandy
      This thesis concerns to spectral gap of random regular graphs and consists of two main con- tributions. First, we prove that almost all bipartite biregular graphs are almost Ramanujan by providing a tight upper bound for ...
    • Spectral Theory of Z^d Substitutions 

      Bartlett, Alan
      In this paper, we generalize and develop results of Queffelec allowing us to characterize the spectrum of an aperiodic substitution in Z^d by describing the Fourier coefficients of mutually singular measures of pure type ...
    • Stable processes with opposing drifts 

      Wright, James M., 1960- (1996)
      A strong Markov process, $W\sp0$, is constructed by a natural linking together of two independent stable processes of type ($\alpha,\ \beta\sb1$) and ($\alpha,\ \beta\sb2$). The drift for a stable process X of type ($\alpha,\ ...
    • Stationary distribution for spinning reflecting diffusions 

      Duarte Espinoza, Mauricio Andres (2012-09-13)
      This dissertation studies two different types of interaction of diffusion processes with the boundary of a domain $DsubRR^n$, which is assumed to be bounded, and of class $C^2(RR^n)$. The first process that is studied is ...
    • Stochastic Approximation with Dynamic Distributions 

      Cutler, Joshua Ross
      We consider first the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems ...
    • Strichartz estimates for the wave equation on Riemannian manifolds of bounded curvature 

      Chen, Yuanlong
      Wave packet methods have proven to be a useful tool for the study of dispersive effects of the wave equation with coefficients of limited differentiability. In this thesis, we use scaled wave packet methods to prove ...
    • Strichartz estimates for wave equations with coefficients of Sobolev regularity 

      Blair, Matthew D (2005)
      Wave packet techniques provide an effective method for proving Strichartz estimates on solutions to wave equations whose coefficients are not smooth. In this work, such methods are used to show Strichartz inequalities for ...
    • Structure and complexity in non-convex and non-smooth optimization 

      Paquette, Courtney
      Complexity theory drives much of modern optimization, allowing a fair comparison between competing numerical methods. The subject broadly seeks to both develop efficient algorithms and establish limitations on efficiencies ...
    • A Tensor-Triangulated Approach to Derived Categories of Non-Noetherian Rings 

      Wolcott, Frank Lucas (2012-09-13)
      We investigate the subcategories and Bousfield lattices of derived categories of general commutative rings, extending previous work done under a Noetherian hypothesis. Maps between rings R → S induce adjoint functors between ...
    • The geometry of uniform measures 

      Nimer, Abdalla Dali
      Uniform measures have played a fundamental role in geometric measure theory since they naturally appear as tangent objects. They were first studied in the groundbreaking work of Preiss where he proved that a Radon measure ...