Our faculty perform original research in many different areas of mathematics.
Abstract Algebra is the branch of mathematics concerned with such structures as
groups,
rings,
fields,
vector spaces, and
modules. Each of these algebraic structures are abstractions of the number systems and arithmetic that we deal with in everyday life. Research in the field of Abstract Algebra is often aimed at trying to understand the deep underlying properties of these abstract algebraic structures.
Faculty who perform research in the area of abstract algebra:
Analysis is the branch of mathematics that includes the theories of limits, derivatives, integrals, infinite series, and continuous functions. It is an extension of the ideas and techniques that were first developed in the study of
Calculus. The modern foundations of mathematical analysis were established in the 17th century by such noted figures as Isaac Newton and Gottfried Leibniz. Today, the techniques of mathematical analysis are applied throughout the physical sciences, in such fields of engineering as
signal processing, and in
quantitative finance.
Faculty who perform research in the area of Analysis:

Enrico AuYeung  pure and applied harmonic analysis, functional analysis

Wei Li  applied analysis, scattering resonances, inverse problems

Karl Liechty  analysis, probability, mathematical physics

David Sher  spectral geometry

Gang Wang  Fourier analysis, probability theory, stochastic processes

Ahmed Zayed  applied harmonic analysis
Combinatorics is the art and science of counting. In all branches of mathematics, the question "How many?" often arises, and the tools of combinatorics can be used to try to answer this question. Fundamentally, combinatorics studies discrete structures as opposed to continuous ones, making the feel of this branch of mathematics quite different from, say, differential equations. Examples of discrete structures include
graphs,
permutations, finite (or countably infinite)
groups, and
cell decompositions of topological spaces.
Faculty who perform research in the area of Combinatorics:
Financial Mathematics is an area of applied mathematics concerned with the mathematical modeling of financial markets.
Faculty who perform research in the area of Financial Mathematics:
Dynamical Systems is the study of systems that change or evolve over time in accordance with some fixed set of rules. Examples of dynamical systems include populations of bacteria that grow at a particular rate, or the motion of a pendulum, which is governed by the rules of Newtonian mechanics.
Faculty who perform research in the area of Dynamical Systems:
Number Theory is the study of the integers and of their arithmetic. Number theory also includes the study of other related number systems where it also makes sense to talk about such concepts as divisibility and
primes. The subject of number theory is renowned for its
many old and simplystated problems that have resisted the best efforts of generations of mathematicians. As a result, modern number theory has come to borrow tools from virtually every branch of mathematics, and has become an incredibly broad and deep field with scores of specializations and applications. Some of the most wellknown applications of elementary theorems from number theory are in the field of
cryptography.
Faculty who perform research in Number Theory:

Nick Ramsey 
padic properties of modular forms, Euclidean rings and ideals
Probability Theory is concerned with the mathematical analysis of random phenomena, and is the mathematical foundation for statistics.
Faculty who perform research in Probability Theory:

Karl Liechty  analysis, probability, mathematical physics

Gang Wang  probability theory, stochastic processes
Statistics is a discipline that uses mathematical and statistical theories to learn from data. Statistics concerns every aspect of data, from the design of experiments, to collecting data, to analyzing data, to presenting findings. Statistical techniques can be applied in a wide variety of disciplines such as biology, business, economics, psychology, public health, and education.
Faculty who perform research in Statistics:

Desale Habtzghi  survival analysis, biostatistics, statistical computing

Juan Hu  geospatial data modeling, massive data analysis, nonparametric modeling

HungChih Ku  statistical genetics, genomewide association studies

Yiou Li  methodologies in statistics and computational mathematics

Claudia Schmegner  mathematical statistics, Bayesian analysis, sequential procedures

Philip Yates  applications of statistics in environmental science, hydrology, and sports; statistics education

Gang Wang  probability theory, stochastic processes, statistics