Faculty Emeriti

Julius Barbanel
Professor of Mathematics, Emeritus
Ph.D., SUNY at Buffalo, 1979
logic, set theory, fair divisionI began my research career in set theory. In particular, my interests were in large cardinal theory, which is the study of very large infinite sets. After about fifteen years in this field, I moved into game theory, focusing specifically on fair division. This involves the allocation of goods among a collection of players, where the goals include both fairness and efficiency. I worked on both abstract existence results and on algorithms in this area. After about fifteen years in this field, I became interested in the ancient Greek foundations of modern mathematics. I developed a general education course on this subject, called “Ancient Greek Mathematics”.

Davide P. Cervone
Professor of Mathematics, Emeritus
Ph.D., Brown University, 1993
simplicial geometry, topologyMy mathematical research centers around polyhedral geometry in three and four dimensions. I have studied immersed surfaces in space that have the fewest possible vertices, and surfaces that have a special cutting property called “tightness”, where any plane will divide the surface into at most two pieces. My most significant result represents one of the few cases in low dimensions where the polyhedral theory differs in a significant way from the smooth case. Much of my work involves computer software that I have developed, and I contribute to a number of open source projects, including MathJax (for displaying math notation on the web) and WeBWorK (an online homework system used at Union). I have been active in exploring how to communicate mathematics in new ways since the earliest days of the internet.

Kathryn Lesh
Professor of Mathematics, Emeritus
Ph.D., Massachusetts Institute of Technology, 1988
algebraic topology, unstable homotopy theoryI study algebraic topology, specifically unstable homotopy theory. I started out by studying the unstable Adams spectral sequence, in a problem related to the Sullivan Conjecture on maps from projective spaces. I returned to the unstable Adams spectral sequence in two later papers on the infinite orthogonal group SO. Most of my recent work has to do with connections between the Goodwillie calculus and the Whitehead Conjecture (proved by Kuhn and Priddy), along with the analogous connections between the orthogonal calculus and an unproved version of the Whitehead Conjecture for connective complex Ktheory.

Susan Niefield
Professor of Mathematics, Emerita
Ph.D., Rutgers University, 1978
exponentiability, double categories, toposes, locales, quantalesMy research involves using category theory, especially adjoint functors, to draw analogies between different areas of mathematics. Much of this work concerns characterizing exponentiable morphisms in nonlocally cartesian closed categories (including topological spaces, locales, toposes, posets, and affine schemes), and finding relationships between these characterizations. I am also interested in structures which capture similarities between different mathematical objects, e.g., quantales (which relate the lattice of ideals of a ring to that of the open subsets of a space) and double categories (which relate topological spaces, locales, quantales, toposes, posets, modules, and small categories).

Kimmo Rosenthal
Professor of Mathematics, Emeritus
Ph.D., State University of New York at Buffalo
category theory, algebra, logicI have been teaching mathematics at Union College for over three decades. Prior to 2000 I published two books and 27 articles on various aspects of category theory. From 20002008 I served as Dean of Studies at the college, overseeing the curriculum and the academic lives of the entire student body. After resigning as Dean, I returned to the mathematics classroom with a renewed vigor and enthusiasm. From 20082020 I regularly taught the FirstYear Preceptorial, a required seminar on critical reading and writing. At the same time my attention turned from mathematical research to writing. I have 20 publications (stories, poems, essays) in various literary journals.

Alan Taylor
Marie Louise Bailey Professor of Mathematics, Emeritus
Ph.D., Dartmouth College, 1975
set theory, logic, simple games, social choice, mathematical political scienceMy graduate training was in the field of mathematical logic, and I spent the first fifteen years of my career doing infinitary combinatorics. Most of my work involved ultrafilters on omega, ideals on uncountable cardinals, and partition theory (including a bit of work with finite Ramsey theory). I spent the following fifteen years with a number of questions from the area of “fair division” and with some topics arising from the theory of voting. Here, I was primarily studying simple games. For the past decade I have returned to set theory with somewhat of a focus on coordinated inference as captured by socalled hat problems.

Karl Zimmermann
Professor of Mathematics, Emeritus
Ph.D., Brown University, 1986
number theory, formal groupsMost of my research is in the area of arithmetic geometry and in particular, formal groups, but more recently, I’ve become interested in a problem related to both formal groups and local (padic) dynamical systems. While thinking about a conjecture of Lubin involving power series that commute under composition, I started working with commuting polynomials that have coefficients in the complex numbers. A complete classification of these polynomials was given around 1920 by Ritt and Julia, working independently. That result is easily stated, but the proof is topological and fairly deep. My current work involves looking at commuting polynomials from an algebraic point of view and trying to apply formal group theoretic techniques, when possible, to gain a better understanding of the problem.

William S. Zwicker
William D. Williams Professor of Mathematics, Emeritus
Research Professor
Ph.D., Massachusetts Institute of Technology, 1976
mathematical logic, set theory, game theory, voting and political power, social choice theory, fair divisionMy early research was in combinatorial set theory, especially large cardinals and ideals and filters on Pκλ. Today, I work on applications of mathematics to the social sciences: voting and social choice, fair division, and cooperative game theory. I’ve enjoyed coauthoring papers with mathematicians, political scientists, economists, and undergraduates from Canada, Catalonia, France, Ireland, Italy, Turkey, Venezuela, and the U.S. I’m on the editorial board of Mathematical Social Sciences and coauthor, with Alan D. Taylor, of the monograph Simple Games (Princeton, 1999). I’m most attracted to fundamental issues in the social sciences that lead to questions of independent combinatorial or geometric interest. For a taste, try our online interactive rubber band voting simulator (with Davide Cervone).
Other Faculty Emeriti
 William Fairchild, Professor Emeritus
 Arnold Seiken, Professor Emeritus
In Memoriam
 Theodore A. Bick, Professor Emeritus
 Lois Bing, Departmental Administrative Assistant
 Linda Jorgensen, Departmental Administrative Assistant
 Edwin Gillette, Professor Emeritus