# Research

## What is Mathematics Research?

Students often wonder what sort of research mathematicians do, and why they do it. Research and teaching are the two most important responsibilities of university faculty--the third being service to the university and community. Although I occasionally sit on dissertation committees for engineers and have coauthored a research paper with bio-engineers, I am mainly a pure mathematician. This means that I am primarily engaged in the discovery of new mathematics (theorems and instructive examples). Geometry, my field of research, has applications in many areas including physics, chemistry, biology, engineering, and computer imaging. However, I am usually not directly involved in finding such applications. If research in pure mathematics seems like art-for-art's-sake, then consider the fact that pure (and even seemingly esoteric) mathematics often proves useful in surprising and unpredictable ways. Without fundamental mathematics there could be no applied mathematics (and, for that matter, no science).

Research contributes to the economic health of the state and the country, but also benefits teaching. Even at the level of calculus, the content of which is hardly affected by current mathematical research, I believe that my involvement in research makes a positive contribution to my teaching. I am sure that I could not be an effective calculus teacher if my mind were not engaged in mathematical problems that are as fresh and challenging for me as calculus is for my calculus students. And for students destined to be at the cutting edge of science, research faculty provide a link between what students learn in the classroom and the forefront of scientific inquiry.

## My Research

My research interests include Riemanian geometry, geometry of singular spaces *a la* A. D. Alexandrov, and uniform spaces. My work also involves topology and geometric approaches to algebraic problems, including homogeneous and symmetric spaces, geometric group theory, geometric aspects of topological groups, covering spaces of locally singular spaces. Collaborators include Valera Berestovskii (Omsk State University, Russia), Urs Lang (ETH, Zurich), and Cornelius Stallman (Augusta State).

In the last several years, I have given many invited lectures, including talks at the Euler Institute in St. Petersburg and Novosibirsk, Russia; CIRM in Luminy, France; Mathematics Research Institute in Oberwolfach, Germany; Max Planck Institute for Mathematics in the Natural Sciences in Leipzig, Germany; and ETH, Zurich, Switzerland.

## Contact Information

**Dr. Conrad Plaut**

Professor, Department Head

Mathematics Department

University of Tennessee

Knoxville TN 37996-1300

Phone: 865-974-4319

Email: cplaut@utk.edu