David McKinney/University Relations

Tyrone Duncan has taught mathematics at KU for 37 years and was recently named one of 17 fellows to the prestigious Internaional Federation of Automatic Control.

# Campus Closeup

## Tyrone Duncan, professor of mathematics

**What’s one thing that would surprise people about your work?** Probably most people assume that a mathematician’s activities are a direct extension of math courses in high school or college, such as solving linear or quadratic equations, differentiation or integration of functions and solving linear differential equations. While some of my work and that of other mathematicians does involve solving equations that are more complicated than those in introductory mathematics courses, an important aspect of mathematical research is the understanding of the minimal structure for a solution method so that the method can be extended to other seemingly different situations. Much of my work considers the understanding and the analysis of stochastic models which can be useful descriptions for many physical phenomena. Thus many of my research results on analysis of models appear in papers published in mathematical journals. While the layperson may think that this output is esoteric, mathematics has played a basic role in many “practical” activities. One such activity is mathematical finance where mathematics has profoundly influenced how large and small investors approach the financial markets. Not only has mathematics provided the guide for investments, but also some successful mathematicians have entered this field and had exceptional success. For example a colleague of mine at one of my former institutions started a hedge fund in 1988 and the fund has never had a losing quarter. He is now ranked No. 30 in Forbes Magazine’s list of the richest people in the U.S.

**You were recently elected one of only 17 fellows of the International Federation of Automatic Control. What does it mean to you to be recognized by a body like this, and what does it say for KU?** It is clearly satisfying to be recognized by one’s peers for research. Research requires patience and often recognition requires even more patience. My election also provides important recognition worldwide for KU because the International Federation of Automatic Control is an organization which has units in about 50 countries.

**How would you describe research areas such as control theory and stochastic processes to a layperson, and how did you become interested in them?** Control theory is the discipline that studies the control of systems. While there are examples of controlled systems from hundreds of years ago, a couple recent ones may be more appropriate. In the 1960s a major impetus for control theory was the space program, especially for the requirements of guidance and control of space vehicles. More recently with the continued size reduction and power increase of computing chips, many items that one interacts with daily have a significant use of control. One example is the automobile where most aspects of an automobile are computer controlled to enhance fuel economy and passenger safety.

Stochastic processes appear in many areas of life. Historically a major motivation for their development was the analysis of games of chance. If one tosses a coin repeatedly, then the time order of the outcomes of heads and tails forms a stochastic process because the outcome of each toss of the coin is not known in advance of the toss. For the last 100 years, financial markets have been modeled by stochastic processes. Many physical phenomena experience some chance occurrences or perturbations so they are often modeled as stochastic processes.

I became interested in control theory through summer jobs in a guidance and control group of an aerospace company when I was an undergraduate. My interest in stochastic processes developed in graduate school by both the problems of communication and control in electrical engineering and the research activities in mathematics at my institution.

**You’ve been at KU for about four decades. Are there any keys to your longevity, and what about KU has made you want to stay?** While this is my 37th year at KU, there are others on campus, even in my department, who have been here longer. I would say that my keys to longevity are a continued active research program and the interaction with students through teaching and research. I have stayed at KU for so long because I have found it satisfying. The KU mathematics department has an outstanding history for almost a century for research that has made it internationally known and respected.