Research Topics
Please contact a faculty member whose research topic below is of interest to you, for example, as the topic of a Math 600 course.
Topic 
Description 
Algorithms
for Direct Search Optimization by: Tom Asaki 
Development, improvement and
analysis of algorithms for nondifferentiable, blackbox and
timesensitive optimization problems. 
SurrogateGuided
Optimization by: Tom Asaki 
Development and analysis of
strategies for surrogate models for time sensitive applications. 
Computational
Problems in Optimization by: Tom Asaki 
Image denoising, data
segmentation, data clustering, variational problems. 
Topics in Mathematical Computing by: Kevin Cooper 
Computational tools and techniques that mathematicians need for success in applied research.

Computational Statistics Algorithms
by: Alan Genz 
Development of efficient algorithms for various computationsl statistics problems.

Multidimensional Numerical Integration
by: Alan Genz 
Development of efficient algorithms for various multidimensional integration problems.

Controllability
Theory of Parabolic PDE's by Multiplicative Controls by: Alex Khapalov 
The course is based on Part I of
the monograph, "A.Y. Khapalov, Controllability of partial differential
equations governed by multiplicative controls, Springer, Lecture Notes
Series, vol. 1995, 2010." 
Controllability
Theory of Swimming Phenomenon by: Alex Khapalov 
The course is based on Part III
of the monograph, "A.Y. Khapalov, Controllability of partial
differential equations governed by multiplicative controls, Springer,
Lecture Notes Series, vol. 1995, 2010." 
Theory of Multivariate Regular Variation by: Haijun Li 
Regular variation of Borel measures, linearoperator stability, MeerschaertScheffler spectral decomposition, point processes and random measures, Poisson point process, BalkemaEmbrechts geometric extreme value theory.

Probability in Banach Spaces
by: Haijun Li 
Banach space valued random variables, Rademacher averages, strong law of large numbers, tightness, type and cotype of Banach Spaces, central limit theorem, comparison theorems, Talagrand's concentration inequalities.

Analytic number theory by: ShengChi Liu 
The distribution of prime numbers; analytic properties of the Riemann's zeta function and the
Dirichlet's Lfunction; prime number theorem for arithmetic progressions; the large sieve inequalities;
the BombieriVinogradov theorem.

Algebraic number theory by: ShengChi Liu 
Algebraic number fields and rings of algebraic integers; arithmetic in algebraic number fields; ideals;
unique factorization of ideals; ideal classes and the class group; finiteness of the class number;
Minkowski’s theorem; Dirichlet’s unit theorem; quadratic and cyclotomic number fields; splitting of
primes in extension fields; Dedekind zeta function and Hecke Lfunctions.

Modular forms by: ShengChi Liu 
The modular group and congruence subgroups; Eisenstein and Poincare series; Hecke operators;
Petersson's trace formula; analytic properties of Hecke Lfunctions; estimation of Fourier coefficients.

Mathematical Modeling of Biological Systems by: Elissa Schwartz 
Analysis and simulation of mathematical models in infectious disease dynamics, including model development, stability analysis, parameter estimation, bifurcation analysis, and stochastics.

Theory
and
Applications
of
Nonnegative Matrices by: Michael Tsatsomeros by: Judi McDonald 
Invariant cones and subspaces,
PerronFrobenius theory, Mmatrices, applications in Markov chains,
optimization, control theory, iterative methods for linear systems. 
Matrices
in
Dynamical
Systems by: Michael Tsatsomeros 
Stability of equilibria, linear
differential systems, linear control theory, controllability,
reachability and observability. 
Combinatorial
and
Quantitative
Matrix
Analysis by: Michael Tsatsomeros by: Judi McDonald 
Graph theory and matrices, sign
and zero/nonzero patterns, allow and require problems:
signsolvability, sign nonsingularity, potential stability. 
Topics
in Analysis by: Kevin Vixie 

Topics
in Harmonic Analysis by: Kevin Vixie 

Topics
in Geometric Measure Theory by: Kevin Vixie 

Fundamental
Theory of Partial Differential Equations by: HongMing Yin 
This topic deals with the
fundamental aspect of partial differential equations. The focus is on
the wellposedness, regularity of solutions and qualitative properties
of the solution for a PDE problem. 
Inverse
and Illposed Problems in Partial Differential Equations by: HongMing Yin 
This topic deals with problems where a coefficient or a source in a partial differential equation is unknown. One needs to find the solution and the coefficient at the same time. This type of problems arises from various applications such as medical imaging, nondestructive detection and discovering material properties. 
Asset
Pricing in Financial Engineering by: HongMing Yin 
This topic deals with the mathematical modeling for various asset classes such as stocks, real estate and currency. The focus is on how the mathematical model can be formed to predict the future price movement. 
Electromagnetic
Fields by: HongMing Yin 
The research for this topic is focused on seeking properties of electromagnetic fields. The fundamental theory is based on Maxwell's equations and their generalization. 