Professors' research interests for Capstone projects (Math 4451)

 

Dr. Adhikari: Differential Equations, Topological Degree Theories and Applications
in Monotone Operator Theory in Banach Spaces, Critical Point Theory.

 

Dr. Cao:  Number theory, including q-series, theta functions, partitions, and continued fractions.

 

Dr. Deng:  Differential geometry of Curves and surfaces

 

Dr. Dillon:  Algebra and geometry, including Lie algebras, elementary algebraic geometry, algebraic curves, affine geometry, projective geometry and related algebraic structures, such as quaternions and octonions.

 

Dr. Edwards:  Markov Chains, Fibonacci and Lucas Numbers and the Golden Ratio, Tiling and Tesselations, The Gamma function, Geometry, Groups and Symmetry,  Linear Algebra and Geometry

 

Dr. Fadyn:  Number Theory, Linear Algebra

 

Dr. Fowler:  Combinatorics

 

Dr. Griffiths:  My research topic of interest is Combinatorics. I enjoy working with permutations, some graph theory, posets, and generating functions.  Basically, this is known as Enumerative Combinatorics.  (I like counting.)

 

Dr. Holliday:  Decompositions of graphs, Graph Theory, Latin squares, modular arithmetic, coding theory, cryptography

 

Dr. Kang:  Mathematical Physics

 

Dr. LeBlanc: Undergraduate mathematics education and mathematical physics

 

Dr. McMorran:  Numerical analysis, Differential Equations, Applied Mathematics

 

Dr. Pascu:  Complex Analysis - Geometric Function Theory.   Special classes of univalent functions (starlike, convex, bounded rotation, etc.); Extensions of the notion of convex/starlike maps and properties of such maps (defined in domains other than the unit disk or its exterior, and without being hydrodynamically normalized), Distortion theorems for classes of univalent functions.  General theory of univalent functions; Conformal mappings, defining and studying the properties of some integral operators which preserve the univalence of a function in the upper half-plane; Maximum principle; Schwarz's lemma, analogues and generalizations; subordination.

 

Dr. Ritter:  Green's Functions methods for linear PDE.s, parabolic PDEs with applications in combustion or chemotaxis (biology), blow up in nonlinear parabolic PDEs, Integral equations-theory of simple linear IE's, applications in combustion, blow up in nonlinear IEs of Volterra type, numerical solution of Volterra IE's, special functions (Bessel, Gamma, Error etc.).  Asymptotic and perturbation methods (algebraic or differential eqns), Math of Financial Derivatives

 

Dr. Vandenbussche:      Graph theory, graph coloring and structures in graphs, algorithms on graphs, combinatorics

 

Dr. Wang: One-Dimensional Dynamics, Fractals, Frames, Wavelets

 

Dr. Xu:  PDEs, Soliton theory and integrable systems.  1. Find the solitary-like solutions of some nonlinear partial differential equations (called soliton equations).  2. Transform PDEs to bi-linear forms.  3. Transform a solution to a new solution of PDEs.  4. Find symmetries of PDEs.  5. Symbolic Computations

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