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. McMorran

Numerical analysis

Differential Equations

Applied Mathematics

Dr. Pace

(1) numerical solution of ordinary differential equations (and systems of these) - error analysis and implementation by computer programs, and also using systems of differential equations to model behavior of mechanical or electrical systems [then solving numerically ]

(2) numerical solution of partial differential equations - error analysis and implementation by computer programs

(3) differential geometry of surfaces (curvature, intrinsic geometry, geodesics)

(4) mathematical crystallography (including symmetry groups) (uses linear algebra and a certain amount of group theory)

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 forclasses 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)

Dr. Wang

One-Dimensional Dynamics, Fractals, Frames, Wavelets

Dr. Xu

Soliton theory and integrable systems.

1. find the solitary-like solutions of some nonlinear partial

   differential equations (called soliton equations).

2. find the so-called Backlund transformation which generates

   new solutions from existing ones to a soliton equation.

3. find the finite-dimensional completely integrable systems

   associated with soliton equations.

4. find symmetries of soliton equations.