NEW PALTZ — Two decades of research spanning three continents and the topography of advanced mathematics has resulted in the publication of Natural Dualities for the Working Algebraist, by State University of New York at New Paltz professor of mathematics and computer science David M. Clark and Brian A. Davey of the department of mathematics at LaTrobe University, Bundoora, Australia. Published in 1998 by the Cambridge University Press, this book is the first thorough exposition of duality theory.
“Using a natural duality, it is often possible to translate difficult algebraic problems into dual topological problems where our geometric intuitions can be brought to bear,” explained Clark. “These topological problems are often easier to solve, and the solutions can then be translated back into solutions of the original algebraic problems via the natural duality.”
Clark and Davey’s bi-continental collaboration began at a conference in Iceland in 1988. With roots in work going back to the 1930s, they pulled together scattered articles and conducted independent research into the nature of coding abstract, symbolic algebras into geometric counterparts. Clark continued his research during a sabbatical in Athens, Greece, where he served as founding dean of New York College. The introductory chapter of the book grew out of a two-month graduate seminar he gave at the University of Bern, Austria. Clark later spent four months in Australia with Davey, where they wrote the book proposal as well as two research papers which helped complete their theories.
“This well-written book will be a valuable resource for algebraists, and an invaluable resource for those determined to advance the current flowering of duality theory itself,” said George McNulty, professor of mathematics at University of South Carolina.