Faculty Emeriti & In Memoriam

Faculty Emeriti

• Julius Barbanel

  

  Professor of Mathematics, Emeritus
  Ph.D., SUNY at Buffalo, 1979
  logic, set theory, fair division

  I 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, topology

  My 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 on-line 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.

• Susan Niefield

  

  Professor of Mathematics, Emerita
  Ph.D., Rutgers University, 1978
  exponentiability, double categories, toposes, locales, quantales

  Website

  My 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 non-locally 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, logic

  I 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 2000-2008 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 2008-2020 I regularly taught the First-Year 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 science

  My 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 so-called hat problems.

• Karl Zimmermann

  

  Professor of Mathematics, Emeritus
  Ph.D., Brown University, 1986
  number theory, formal groups

  Most 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 (p-adic) 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 division

  My 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 co-authoring 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 co-author, 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).