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# Research Overview

As the term "mathematical sciences" correctly suggests, pure mathematics, applied mathematics, statistics, and mathematics education coexist harmoniously within the Department. This is also reflective of the varied research interests which exist in our Department. As with any quality mathematics department in the U.S., the strength of our Department depends inextricably on the strength of the research programs of the faculty and the soundness of our academic programs. Increasingly, the tools-the concepts and techniques-of mathematics are playing a vital role in the advancement of science and technology. As these tools are discovered, developed, and refined through mathematical research, they also feed into a broader effort in the training of technical personnel in which all mathematics Departments participate. Faculty research is essential in fostering excellence in our training of undergraduate and graduate students.

Owing to our extraordinarily successful recruitment efforts during the past decade, we have been able to significantly upgrade the quality of our faculty. The Department now has a strong and talented faculty with research programs covering many important areas in pure and applied mathematics, as well as in statistics. Currently, these areas of strength include: Index Theory, Operator Algebras, Noncommutative Geometry, and Differential Geometry; Dynamical Systems; Mathematical Physics; Applied and Computational Mathematics; and Statistics. The diversity of our faculty's research indeed mirrors the intellectual trends of mathematics in a time of burgeoning applications.

## Research Expertise

Current research is being undertaken in the following areas:

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