Department of Mathematics (MU)
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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Locally semisimple representations of quivers
(University of MissouriColumbia, 2016)In this dissertation, we solve a conjecture raised by Victor Kac in 1982 concerning the socalled locally semisimple representations of quivers. 
Properties of frames and relationships between them with emphasis on subframes and unconditional convergence
(University of MissouriColumbia, 2016) 
Stability of planar fronts for a class of reaction diffusion systems
(University of MissouriColumbia, 2016)The purpose of this thesis is to study stability of onedimensional traveling waves and multidimensional planar fronts as well as spaceindependent steady states for a class of reaction diffusion systems that arise in ... 
Maximal Fourier integrals and multilinear multiplier operators
(University of MissouriColumbia, 2016) 
The Dirichlet problem for elliptic and degenerate elliptic equations, and related results
(University of MissouriColumbia, 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 semigroups and their gradients, and then we get Lp bounds for ... 
Weak Hardy spaces and paraproducts
(University of MissouriColumbia, 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
(University of MissouriColumbia, 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
(University of MissouriColumbia, 2016) 
A foliated SeibergWitten theory
(University of MissouriColumbia, 2016)This dissertation set out to investigate a generalization of SeibergWitten theory from fourdimensional manifolds to fourcodimensional Riemannian foliations. SeibergWitten theory was originally born out of the String ... 
GITequivalence and semistable subcategories of quiver representations
(University of MissouriColumbia, 2016)The main investigation in this thesis is to determine when two weights give rise to the same semistable 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
(University of MissouriColumbia, 2016) 
Rectifiability and harmonic measure
(University of MissouriColumbia, 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 recti fiable sets. These structure ... 
Quasilinear elliptic equations with subnatural growth aand nonlinar potentials
(University of MissouriColumbia, 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
(University of MissouriColumbia, 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
(University of MissouriColumbia, 2015)Trace and extension theory lay the foundation for solving a plethora of boundary value problems. In developing this theory, one typically needs wellbehaved extension operators from a specified domain to the entire Euclidean ... 
Topics in geometric analysis and harmonic analysis on spaces of homogeneous type
(University of MissouriColumbia, 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 ... 
Agedependent Branching Processes and Applications to the LuriaDelbrck Experiment
(University of MissouriColumbia, 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
(University of MissouriColumbia, 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 ... 
QuasiMetric Geometry
([University of MissouriColumbia], 2014) 
Expectation of pnorm of random matrices with heavy tails
([University of MissouriColumbia], 2014)The pnorm (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: ...