# John Kennison, Ph.D.

Professor
Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610-1477

(508) 793-7394 phone
email: jkennison@clarku.edu
Personal Web Page: http://math.clarku.edu/~jkennison/

Professor Kennison received a B.S. from Queens College in 1959 and an A.M. and Ph.D. from Harvard University in 1960 and 1963, respectively. He has been with Clark since 1963.

## Current Research and Teaching

Professor Kennisonâ€™s research interests are in category theory and topology.

Learning Mathematics:

Mathematical concepts tend to be abstract but they can become familiar and comfortable when you understand them intuitively, logically and technically. You can get an intuitive feel for them by seeing how they are used and by exploring examples. Techniques can be mastered through practice. The logical aspects, such as definitions and theorems, are often stated in a precise way that may be hard to digest. So you need to read the formal parts of mathematics carefully and work your way through them slowly. Try to convince yourself that the definitions agree with your intuitive understanding; that the theorems are plausible and their proofs are convincing. Of course anyone can get stuck when trying to do these things. All my life I have been excited by mathematical discovery, but sometimes I get stuck on simple points. And while I have learned how to get myself unstuck, you may need to talk things over with someone who knows the material. At Clark, our tutors and our faculty are open to your questions.

## My Research Interests:

My specialties are topology and category theory. Topology is a way of studying spaces by using limits rather than straight lines and angles. Category theory is a way of doing math by seeing how one mathematical object can be mapped into another. I have been using both of these tools to analyze dynamical systems, which can be thought of as systems whose structures change over time. A dynamical system may eventually arrive at a steady state or it can cycle through a fixed sequence of states or it can become chaotic and change in an irregular way, possibly getting arbitrarily close to any possible state without ever settling down. Category theory suggests that there is a spectrum of possible outcomes and I have shown that sometimes this spectrum is a topological space.

A dynamical system seems to evolve and I have helped write a paper about the evolution of altruism. I have also co-authored a paper about the use of locales (which are related to topology) to analyze seemingly ambiguous statements that might be true only in part of the locale. For example, some statements might be true in some cultural contexts but false in other contexts. Perhaps there is a locale of all possible cultural contexts.

## Recent Publications

(Co-authors with * are colleagues at Clark)

(with Michael Barr and Robert Raphael) Searching for Absolute CR-epic Spaces

to appear, Canadian Journal of Math.

(with Nicholas Thompson* and David Joyce* et al) My Way or the Highway: a more Naturalistic Model of Altruism tested in an iterative Prisonerâ€™s Dilemma, Journal of Artificial Societies and Social Stimulation, Vol 9 (2006).

Spectra of Finitely Generated Boolean Flows, TAC (Theory and Applications of Categories), Vol 16 (2006), p.434-459.

(with David Joyce*) Mathematical Concepts for Analyzing Ambiguous Situations, Estudios de Psicologia, Vol 27(2006) p. 85-100.

The Cyclic Spectrum of a Boolean Flow, TAC, Vol 10(2002) p392-409.