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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Rectifiability and harmonic measure
(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: ... 
On unimodality of Hilbert functions of Artinian level algebras of codimension 3 and type 2 and 3
([University of MissouriColumbia], 2014)We prove the unimodality of the Hilbert Function for some classes of codimension three graded algebras of CohenMacaulay types 2 and 3. The method of proof uses the explicit structure theorems similar to the structure ... 
Results on the Collatz Conjecture
([University of MissouriColumbia], 2014)Given a starting value, we can create a sequence using the rule that if the previous number, x, is even, then the next number is [x/2], and if the previous number, x, is odd, then the next number is [(3x+1)/2]. The collatz ... 
Generating sequences of valuations and applications
([University of MissouriColumbia], 2014) 
Irrational behavior of algebraic discrete valuations
([University of MissouriColumbia], 2014)We construct a family of algebraic discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasipolynomial and a bounded function. We further show that the set of multiplicities ... 
Lorentzian warped products and static spacetimes
(University of MissouriColumbia, 1985) 
A vector treatment of the projective properties of plane curves
(University of Missouri, 1916) 
Limit of many molecules dynamics with rigorous macroscopic results
(University of MissouriColumbia, 2013)The thesis builds on recent ideas that combine work by C.B. Morrey (1955) and D.W. Jepsen & D. ter Haar (1962) with more recent analytic techniques: measure disintegration, PDEs for measures, etc. (M.I. Vishik & A.V. ... 
Stability estimates for semigroups and partly parabolic reaction diffusion equations
(University of MissouriColumbia, 2013)The purpose of my dissertation is the application of the methods of abstract theory of strongly continuous operator semigroups (and of evolution semigroups in particular) to study of the spectral properties of a class of ... 
Frames and projections
(University of MissouriColumbia, 2013)In this dissertation we explore several ways in which the concept of projections arise infinite frame theory. In the first chapter we show that the Paulsen problem from frame theory is equivalent to a long standing open ... 
Groupoids and semigroupoids
(University of MissouriColumbia, 2013)The theory of semigroupoids and groupoids makes the transition between arbitrary sets and groups. The usefulness of developing theory stems from various applications where a group structure is lacking, yet there exists ... 
Stochastically perturbed NavierStokes system on the rotating sphere
(University of MissouriColumbia, 2013)We show the existence and uniqueness of an invariant measure for the kickforced NavierStokes system on the 2dimensional sphere, first without deterministic force and then with a timeindependent deterministic force. The ...