Now showing items 137-156 of 188

    • The Radiative Transfer Equation in Photoacoustic Imaging 

      Patrolia, Lee (2013-07-25)
      Photoacoustic tomography is a rapidly developing medical imaging technique that combines optical and ultrasound imaging to exploit the high contrast and high resolution of the respective individual modalities. Mathematically, ...
    • Random combinatorial processes 

      Richey, Jacob
      We study four problems in combinatorial probability, namely: activated random walk, an interacting particle process; a phase transition for Wishart matrices, a model of a random geometric graph; the Boolean intersection ...
    • Random Permutations and Simplicial Complexes 

      Fowler, Christopher F
      We study the asymptotic behavior of distributions on two different combinatorial objects, permutations and simplicial complexes. First we study strong α-logarithmic measures on the symmetric group, including the well- ...
    • Random recursion 

      Junge, Matthew S.
      We study the limiting behavior of three stochastic processes. Two are interacting particle systems, the frog model and coalescing random walk. We work out transience and recurrence properties on various graphs. The last ...
    • Rational Point on Conic Bundles 

      Roven, Sam Milan
      In this paper, we focus on obstructions to the existence of rational points for a special class of algebraic varieties. In particular, we consider the case where $\pi \colon X \rightarrow \PPP_k^1$ is a smooth conic bundle ...
    • Realization spaces of polytopes and matroids 

      Wiebe, Amy
      Chapter 1 describes several models for the realization space of a polytope. These models include the classical model, a model representing realizations in the Grassmannian, a new model which represents realizations by slack ...
    • Rectifiability via curvature and regularity in anisotropic problems 

      Goering, Max Landon
      Understanding the geometry of rectifiable sets and measures has led to a fascinating interplay of geometry, harmonic analysis, and PDEs. Since Jones' work on the Analysts' Traveling Salesman Problem, tools to quantify the ...
    • The regularity of Loewner curves 

      Tran, Huy Vo
      The Loewner differential equation, a classical tool that has attracted recent attention due to Schramm-Loewner evolution (SLE), provides a unique way of encoding a simple 2-dimensional curve into a continuous 1-dimensional ...
    • Regularity results for the variable-coefficient Plateau problem 

      Simmons, David
      We study almost-minimizers of anisotropic surface energies defined by a Holder continuous matrix of coefficients acting on the unit normal direction to the surface. In this generalization of the Plateau problem, we prove ...
    • Representations and Support Theory for Bosonized Quantum Complete Intersections 

      Courts, Nicolas
      Support theories are frequently used by representation theorists when trying to understand module categories with complicated structure. We associate to an algebra A a variety where the topological structure is determined ...
    • Results on singularities of pairs 

      Prelli, Lorenzo
      Singularities of algebraic varieties have been studied extensively, and recently also the properties of singularities of pairs have been investigated. This thesis presents several results on singularities of different kinds ...
    • Rough Collisions 

      Rudzis, Peter Francis
      A rough collision law describes the limiting contact dynamics of a pair of rough rigid bodies, as the scale of the rough features (asperities) on the surface of each body goes to zero. The class of rough collision laws is ...
    • 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 ...