Faculty members in MU’s Department of Mathematics are actively engaged in research in both theoretical and applied mathematics. With a wide range of research interests, they prepare students for careers in teaching, medicine, scientific research, business, finance and a host of other fields. Working side by side with students, faculty members stress learning how to learn and keep up with the future of mathematics. With 39 regular faculty members working in a variety of fields, the department provides a comprehensive understanding of mathematics. The faculty’s research and teaching are supported by postdoctoral fellows and visiting faculty.

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  • Stability and instability results for the 2D a-Euler equations 

    Vasudevan, Shibi Kapisthalam (University of Missouri--Columbia, 2017)
    We study stability and instability of time independent solutions of the two dimensional a-Euler equations and Euler equations; the a-Euler equations are obtained by replacing the nonlinear term (u · ?)u in the classical ...
  • Large-amplitude solitary water waves with discontinuous vorticity 

    Akers, Adelaide (University of Missouri--Columbia, 2017)
    Consider a two-dimensional body of water with constant density which lies below a vacuum. The ocean bed is assumed to be impenetrable, while the boundary which separates the uid and the vacuum is assumed to be a free ...
  • Topics in spectral theory of differential operators 

    Sukhtaiev, Selim (University of Missouri--Columbia, 2017)
    This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of self-adjoint extensions of partial differential operators, and computing the number of negative ...
  • A sublinear version of the Schur Test and weighted norm inequalities 

    Quinn, Stephen (University of Missouri--Columbia, 2017)
    In this thesis, we study the sublinear elliptic equations of the form (-?u - u qs = 0 s - a.e. on ? u = 0 on ??, where 0 greater than q less than 1 and s is a positive Borel measure on ?. Our results show that, under ...
  • Outer products and frame coefficients 

    Pinkham, Eric (University of Missouri--Columbia, 2017)
    In this dissertation, we will examine two distinct areas of frame theory. The first will be the area of outer products. In particular, we will examine the spanning and independence properties of the collection {fif * i ...
  • Harmonic functions and the Dirichlet problem 

    Mayfield, Caleb James (University of Missouri--Columbia, 2017)
    Let ? be an open and connected subset of the complex plane. A real valued function u : ? ? R is said to be harmonic if it has continuous first and second partial derivatives and satisfies Laplaces equation ?u = ? 2u ?x2 + ...
  • Conformal mappings and the Schwarz-Christoffel transformation 

    Heinen, Rebecca (University of Missouri--Columbia, 2017)
    Let ? be an open and connected set in the complex plane. A mapping f : ? ? C is said to be conformal at a point z0 if it preserves angles and orientation between curves intersecting at z0. We discuss tangent lines and their ...
  • Uniform bounds in f-finite rings and their applications 

    Polstra, Thomas Marion (University of Missouri--Columbia, 2017)
    This dissertation establishes uniform bounds in characteristic p rings which are either F-finite or essentially of finite type over an excellent local ring. These uniform bounds are then used to show that the Hilbert-Kunz ...
  • Perinormality in Polynomial and Module-Finite Ring Extensions 

    McCrady, Andrew (University of Missouri--Columbia, 2017)
    In this dissertation we investigate some open questions posed by Epstein and Shapiro in [9] regarding perinormal domains. More specifically, we focus on the ascent/descent property of perinormality between "canonical" ...
  • Exponential sums, character sums, sieve methods and distribution of prime numbers 

    Guo, Victor Zhenyu (University of Missouri--Columbia, 2017)
    This thesis is focus on the methods of exponential sums and sieve methods applying to distribution of primes numbers in several forms, such as Piatetski-Shapiro primes, Beatty sequences, almost primes and primes in arithmetic ...
  • Integration by parts formulas for higher order operators and applications to boundary value problems 

    Essner, Kayla (University of Missouri--Columbia, 2016)
    Green formulas for differential operators are important tools in the study of Partial Differential Equations. The first such formula, published in 1828, was obtained by George Green for the Laplacian in three dimensions. ...
  • 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.
  • Calderon-Zygmund theory for singular integral operators associated with second-order elliptic partial differential systems on rough subdomains of Riemannian manifolds 

    Schmutzler, Brock Allen (University of Missouri--Columbia, 2016)
    This dissertation is a treatise on the theory of Calderon-Zygmund type singular integral operators capable of handling boundary layer potentials arising naturally in the treatment of elliptic boundary value problems on ...
  • 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)

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