College of Arts and Sciences

Department of Mathematics

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, black-box and time-sensitive optimization problems.


Surrogate-Guided 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, linear-operator stability, Meerschaert-Scheffler spectral decomposition, point processes and random measures, Poisson point process, Balkema-Embrechts 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: Sheng-Chi Liu
The distribution of prime numbers; analytic properties of the Riemann's zeta function and the Dirichlet's L-function; prime number theorem for arithmetic progressions; the large sieve inequalities; the Bombieri-Vinogradov theorem.


Algebraic number theory
by: Sheng-Chi 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 L-functions.


Modular forms
by: Sheng-Chi Liu
The modular group and congruence subgroups; Eisenstein and Poincare series; Hecke operators; Petersson's trace formula; analytic properties of Hecke L-functions; 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, Perron-Frobenius theory, M-matrices, 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: sign-solvability, 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: Hong-Ming Yin
This topic deals with the fundamental aspect of partial differential equations. The focus is on the well-posedness, regularity of solutions and qualitative properties of the solution for a PDE problem.


Inverse and Ill-posed Problems in Partial Differential Equations
by: Hong-Ming 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: Hong-Ming 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: Hong-Ming 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.
Department of Mathematics, PO Box 643113, Neill 103, Washington State University, Pullman WA 99164-3113 Phone: 509-335-3926 Fax: 509-335-1188 Contact Us