Recent Submissions

  • Non-local operators, jump diffusions and Feynman-Kac tranforms 

    Wang, Lidan
    Non-local operators are analytically defined by integrals over the whole space, hence hard to study certain properties. This thesis studies inverse local times at $0$ of one-dimensional reflected diffusions on $[0, ...
  • Novel uses of the Mallows model in coloring and matching 

    Levy, Avi William
    A natural model of a highly ordered random ranking is the Mallows model. Disorder is measured by the number of inversions; these are pairs of elements whose order is reversed. The Mallows model assigns to each ranking of ...
  • Bin packing, number balancing, and rescaling linear programs 

    Hoberg, Rebecca Anne
    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 ...
  • Bispectral Operator Algebras 

    Casper, William Riley
    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 $x$ ...
  • Algorithms in Discrepancy Theory and Lattices 

    Ramadas, Harishchandra
    This thesis deals with algorithmic problems in discrepancy theory and lattices, and is based on two projects I worked on while at the University of Washington in Seattle. A brief overview is provided in Chapter 1 (Introduction). ...
  • A Survey of Tverberg Type Problems 

    Thng, Ivana
    Tverberg's theorem, which celebrates its fiftieth anniversary this year, is a central result in the fields of discrete geometry and topological combinatorics. Proved in 1966, it was a major step in solving questions whether, ...
  • Problems in Algebraic Vision 

    Lee, Hon Leung
    This thesis studies several fundamental mathematical problems that arise from computer vision using techniques in algebraic geometry and optimization. Chapters 2 and 3 consider the fundamental question of the existence of ...
  • On f-vectors of polytopes and matroids 

    Samper Casas, Jose Alejandro
    The f-vector of a simplicial complex is a fundamental invariant that counts the number of faces in each dimension. A natural question in the theory of simplicial complexes is to understand the relationship between the ...
  • 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 ...
  • 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 ...
  • On T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions 

    Van Huele, Yannick
    For certain Zp-extensions of abelian number fields, we study the Iwasawa module associated to the ideal class groups. We show that generic Zp-extensions of abelian number fields are T-semisimple. We also construct the ...
  • On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities 

    Merhej, Jessica
    A central question in geometric measure theory is whether geometric properties of a set translate into analytical ones. In 1960, E. R. Reifenberg proved that if an $n$-dimensional subset $M$ of $\mathbb{R}^{n+d}$ is well ...
  • Formal group laws and hypergraph colorings 

    Taylor, Jair Patrick
    This thesis demonstrates a connection between formal group laws and chromatic symmetric functions of hypergraphs, two seemingly unrelated topics in the theory of symmetric functions. A formal group law is a symmetric ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Geometry and Optimization of Relative Arbitrage 

    Wong, Ting Kam Leonard
    This thesis is devoted to the mathematics of volatility harvesting, the idea that extra portfolio growth may be created by systematic rebalancing. First developed by E. R. Fernholz in the late 90s and the early 2000s, ...
  • 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 ...
  • On Selmer groups and factoring p-adic L-functions 

    Palvannan, Bharathwaj
    Samit Dasgupta has proved a formula factoring a certain restriction of a 3-variable Rankin-Selberg p-adic L-function as a product of a 2-variable p-adic L-function related to the adjoint representation of a Hida family and ...
  • Aspects of Markov Chains and Particle Systems 

    Ganguly, Shirshendu
    The thesis concerns asymptotic behavior of particle systems and the underlying Markov chains used to model various natural phenomena. The objective is to describe and analyze stochastic models involving spatial structure ...

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