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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Several problems on moduli stacks of hyperelliptic curves
(University of MissouriColumbia, 2023)The main objects to investigate in this thesis are the moduli stacks of smooth hyperelliptic curves of genus g, denoted by Hg, and its DeligneMumford compactification Hg in Mg. A result by Kleiman and Lonsted says that ... 
Global bifurcation of antiplane shear equilibria
(University of MissouriColumbia, 2023)Bifurcation theoretic methods are used to construct families of solutions for two problems arising in nonlinear elasticity. These solution curves are shown to exhibit interesting phenomena that are both mathematically ... 
The asymptotic Samuel function of a filtration
(University of MissouriColumbia, 2023)We extend the asymptotic Samuel function of an ideal to an arbitrary filtration of a Noetherian ring. We observe that although many properties that hold true in the ideal case are true for filtrations, there are many ... 
On toric varieties and toric stacks
(University of MissouriColumbia, 2023)In this dissertation, we prove a number of results about toric varieties by utilizing Cox's construction of a toric variety as a good quotient of an open subset of affine space by the action of a diagonalizable group. Our ... 
Relative subrepresentation theorem for a finite central extension of a reductive group
(University of MissouriColumbia, 2023)Jacquet's subrepresentation theorem asserts that any irreducible admissible representation of a reductive padic group is a subrepresentation of IndG P ([tau]), where P is a parabolic subgroup of G and [tau] is a cuspidal ... 
Algorithmfree methods in fusion frame construction
(University of MissouriColumbia, 2022)Over the past decade numerous papers have been published with novel methods for proving the existence of and constructing fusion frames under various restrictions on the ambient Hilbert space, set of subspace dimensions, ... 
Partial connections and contact instantons on contact manifolds
(University of MissouriColumbia, 2022)[EMBARGOED UNTIL 8/1/2023] We study partial connections that are defined on a vector bundle E over a contact distribution H of a contact manifold (M2m+1; [zero with middle tilde]) by adapting the Rumin complex of the ... 
Global bifurcation and stability of solitary waves in twolayer water
(University of MissouriColumbia, 2022)The present work concerns two mathematical problems on wave in a stratified body of water governed by the incompressible Euler equations. In the first part, we present a largeamplitude existence theory for twodimensional ... 
A Quiver Invariant theoretic approach to radial isotropy and the Paulsen problem for matrix frames
(University of MissouriColumbia, 2022)In this dissertation, we view matrix frames as representations of quivers and study them within the general framework of Quiver Invariant Theory. We are particularly interested in radial isotropic and Parseval matrix frames. ... 
Simultaneous local resolution along a rational valuation in two dimensional positive characteristic function fields
(University of MissouriColumbia, 2022)We consider the condition that a germ of an algebraic mapping of nonsingular surfaces can be made finite, after sufficient blowing up along a nondiscrete rational rank 1 valuation. This problem has been solved in the ... 
Madic perturbations in Noetherian local rings
(University of MissouriColumbia, 2021)The purpose of this thesis is to develop methods for the study madic stability in an arbitrary Noetherian local ring. A key role is played by the ArtinRees lemma. Using these techniques we establish new results about the ... 
Structural features of persistent homology and their algorithmic transformations
(University of MissouriColumbia, 2021)We reexamine the theory and orthodox methods that underlie the study of persistent homology, particularly in its calculation of homological cycle representatives that are associated to persistence diagrams. A common ... 
Linear and multilinear spherical maximal functions
(University of MissouriColumbia, 2020)In dimensions n [greater than or equal to] 2 we obtain Lp1(Rn) x ... x Lpm(Rn) to Lp(Rn) boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples ... 
Volumes of line bundles on schemes
(University of MissouriColumbia, 2021)The volume of a line bundle is an invariant defined in terms of a limit superior. It is a fundamental question whether this limit superior is a limit. It has been shown that this is always the case on generically reduced ... 
Adams inequalities with exact growth condition : on Rn and the Heisenberg group
(University of MissouriColumbia, 2020)In this thesis we prove sharp Adams inequality with exact growth condition for the Riesz potential as well as the more general strictly Rieszlike potentials on R[superscript n]. Then we derive the MoserTrudinger type ... 
Mathematical and computational modeling of fluid flow with applications in ophthalmology and geoscience
(University of MissouriColumbia, 2020)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Complex systems in our life can be translated to mathematical models whose solutions can help us to predict the behavior of the system. Disease in eye ... 
Stochastic forms of functional isoperimetric inequalities
(University of MissouriColumbia, 2021)The BrunnMinkowski and PrekopaLeindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions, so it seems that ... 
Critical perturbations of elliptic operators by lower order terms
(University of MissouriColumbia, 2021)In this work we study issues of existence and uniqueness of solutions of certain boundary value problems for elliptic equations in the upper halfspace. More specifically we treat the Dirichlet, Neumann, and Regularity ... 
Entropy minimization, convergence, and Gibbs ensembles (local and global)
(University of MissouriColumbia, 2021)We approach the subject of Statistical Mechanics from two different perspectives. In Part I we adopt the approach of Lanford and MartinLof. We examine the minimization of information entropy for measures on the phase space ... 
Frames with desired angle properties
(University of MissouriColumbia, 2020)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] The purpose of this dissertation is to study frames with desired angle properties. More precisely, we study the subspace packing problem, harmonic ...