The items in this collection are the theses and dissertations written by students of the Department of Mathematics. Some items may be viewed only by members of the University of Missouri System and/or University of Missouri-Columbia. Click on one of the browse buttons above for a complete listing of the works.

Recent Submissions

  • Locally semi-simple representations of quivers 

    Kline, Daniel (University of Missouri--Columbia, 2016)
    In this dissertation, we solve a conjecture raised by Victor Kac in 1982 concerning the so-called locally semi-simple representations of quivers.
  • Stability of planar fronts for a class of reaction diffusion systems 

    Yang, Xinyao (Researcher on mathematics) (University of Missouri--Columbia, 2016)
    The purpose of this thesis is to study stability of one-dimensional traveling waves and multidimensional planar fronts as well as space-independent steady states for a class of reaction diffusion systems that arise in ...
  • Maximal Fourier integrals and multilinear multiplier operators 

    Nguyen, Hanh Van (Researcher on mathematics) (University of Missouri--Columbia, 2016)
    The first topic of this dissertation is concerned with the L^2 boundedness of a maximal Fourier integral operator which arises by transferring the spherical maximal operator on the sphere S^n to a Euclidean space of the ...
  • The Dirichlet problem for elliptic and degenerate elliptic equations, and related results 

    Le, Phi Long (Postdoctoral fellow) (University of Missouri--Columbia, 2016)
    In this thesis, we first prove the solvability of Dirichlet problem with Lp data on the boundary for degenerate elliptic equations. Second, We obtain Lp bounds semi-groups and their gradients, and then we get Lp bounds for ...
  • Weak Hardy spaces and paraproducts 

    He, Danqing (University of Missouri--Columbia, 2016)
    The purpose of this dissertation is to provide a new square function characterization of weak Hardy spaces in the full range of exponents possible and use this characterization in applications on endpoint estimates for ...
  • Some results in convex geometry 

    Spencer, Patrick, 1987- (University of Missouri--Columbia, 2016)
    This thesis is divided into four parts. The first part is about proving that the unit ball of the Lorentz space is not an intersection body for dimension greater than or equal to 5 and q > 2. We go on to explain the ...
  • Subsequences of frames and their operators 

    Lynch, Richard G. (Richard Gerald) (University of Missouri--Columbia, 2016)
  • A foliated Seiberg-Witten theory 

    Renner, Andrew (University of Missouri--Columbia, 2016)
    This dissertation set out to investigate a generalization of Seiberg-Witten theory from four-dimensional manifolds to four-codimensional Riemannian foliations. Seiberg-Witten theory was originally born out of the String ...
  • GIT-equivalence and semi-stable subcategories of quiver representations 

    Granger, Valerie, 1985- (University of Missouri--Columbia, 2016)
    The main investigation in this thesis is to determine when two weights give rise to the same semi-stable subcategory in the case of representations of quivers. This question was answered via explicit construction by Ingalls, ...
  • Inertial Chow rings and a new asymptotic product 

    Coleman, Thomas, 1988- (University of Missouri--Columbia, 2016)
    For any toric Deligne-Mumford stack X and equivariant vector bundle V , we can define an two associative inertial products. We give a ring presentation for the inertial Chow ring of X under each of these products and compute ...
  • Rectifiability and harmonic measure 

    Bortz, Simon, 1987- (University of Missouri--Columbia, 2016)
    This dissertation is concerned with the interplay of the geometry of the boundary of a given domain (or open set) and its harmonic measure. First, we prove structure theorems for uniformly rectifiable sets. These structure ...
  • Quasilinear elliptic equations with sub-natural growth aand nonlinar potentials 

    Cao, Dat Tien (University of Missouri--Columbia, 2015)
    Necessary and sufficient conditions for the existence of finite energy and weak solutions are given. Sharp global pointwise estimates of solutions are obtained as well. We also discuss the uniqueness and regularity properties ...
  • Frames and applications: distribution of frame coeficients, integer frames and phase retrieval 

    Woodland, Lindsey M. (University of Missouri--Columbia, 2015)
    The present dissertation is divided into two main areas: frame theoretic results and applications of frames. In particular, the beginning half develops the first detailed theory of the distribution of frame coefficients. ...
  • Trace/extension operators in rough domains and applications to partial differential equations 

    Brewster, Kevin (University of Missouri--Columbia, 2015)
    Trace and extension theory lay the foundation for solving a plethora of boundary value problems. In developing this theory, one typically needs well-behaved extension operators from a specified domain to the entire Euclidean ...
  • Topics in geometric analysis and harmonic analysis on spaces of homogeneous type 

    Alvarado, Ryan (University of Missouri--Columbia, 2015)
    The present dissertation consists of three main parts. One theme underscoring the work carried out in this dissertation concerns the relationship between analysis and geometry. As a first illustration of the interplay ...
  • Age-dependent Branching Processes and Applications to the Luria-Delbrck Experiment 

    Oveys, Hesam (University of Missouri--Columbia, 2015)
    Microbial populations adapt to their environment by acquiring advantageous mutations, but in the early twentieth century, questions about how these organisms acquire mutations arose. The experiment of Salvador Luria and ...
  • Counterexamples to Strichartz Type Inequalities 

    Alhazaa, Khalifa (University of Missouri--Columbia, 2013)
    The study of Strichartz s inequality is very important in the theory of nonlinear Shrodinger equations. The inequalities do not hold for all choice of constants. Many cases were settled. for instance, some cases were settled ...
  • Quasi-Metric Geometry 

    Brigham, Dan ([University of Missouri--Columbia], 2014)
  • Expectation of p-norm of random matrices with heavy tails 

    Vaidyanathan, Chandrasekar, 1975- ([University of Missouri--Columbia], 2014)
    The p-norm (p > 2) of a random matrix whose entries are gaussian, subgaussian and log concave have been studied previously. We conjecture the following generalization of the above results for heavy tailed random matrices: ...

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