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”.

• 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).

• 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.