Broad categories of ongoing research activities are carried out in the Department of Mathematics of Hampton University (HU). The major research areas and interests include: (1) Stochastic Processes and Times Series Analysis; (2) Computational Fluid Dynamics (CFD), Applied CFD, and Fluid Mechanics; (3) Fusion, Plasma Physics and Nonlinear Dynamics; (4) Computational Sciences and Applied Numerical Analysis; and (5) Applied Statistical Methods - reliability and life data analysis, environmental data analysis and design of experiments.

The following is a brief description of some of the research projects accomplished or currently being carried out in the department:

1. Four faculty members have more than 50 years of combined experience working in the area of stochastic processes and times series analysis. This group is currently pursuing research on stationary stochastic process problems. The work in this area includes infinite dimensional processes, multivariate processes, p-th order processes, stable processes, and random fields. Recently they have directed their research to exploring various classes of non-stationary stochastic processes. Over the last ten years the Office of Naval Research, NASA and the U.S. Army have supported most of these research activities through grants.
2. There are four faculty members with over 50 years of technical experience in the areas of CFD, Applied CFD and Fluid Mechanics. This group has accomplished several research and developmental projects under the sponsorship of NASA, U.S. Army and U.S. Navy through contracts and grants. The work includes developing CFD computer codes for aerodynamics problems, developing sensitivity derivative versions of CFD codes for aircraft design applications, and performing CFD analysis on advanced aerodynamics problems.
3. The Mathematics Department houses the HU Center for Fusion Research and Training which is jointly staffed from the faculty of the Mathematics and the Physics Departments. The center conducts state-of-the-art research in the area of controlled thermonuclear fusion, and trains African-American scholars in this key energy science of the next century. The center has collaborations with Columbia University, General Atomics and Princeton Plasma Physics Laboratory. The emphasis of the center's fusion research is magnetic confinement systems, especially the tokamak device and applications of nonlinear dynamics to the problems of fusion. The center is supported by a research grant from the US Department of Energy - Office of Fusion Research.
4. In the areas of Computational Sciences, two faculty members conduct research projects in high-performance computing under the sponsorship of NASA and the U.S. Army. Research includes investigating the performance of massively parallel high-performance computers in aerodynamics applications, computational solidification using a phase field approach and parallel algorithms for optimal subset selection of observation variables.
5. Two faculty members have over 40 years of experience as corporate statisticians at a world-class FORTUNE 500 company. In this capacity, the major research focus has been in the development of new statistical analysis software tools and methods for predicting the life performance of products ranging from X-ray tubes for medical diagnostic equipment to large locomotive systems. The faculty members have technical expertise in teaming with engineers, scientists, managers and others to successfully apply mathematical and statistical methods to real-world problems in manufacturing, financial services, and high-technology businesses. Other significant research work has been in the area of designing sampling plans and implementing advanced data analysis techniques for environmental applications.

Graduate students are an integral part of the department's research activities. They work as graduate research assistants under the guidance of first-class research faculty. Research activities are supported through grants from federal agencies and national research laboratories, including the National Science Foundation, Office of Naval Research, U.S. Army Research Office, Air Force Office of Scientific Research, NASA, and Department of Energy.