Peter McMullen, PhD, DSc
Emeritus Professor

My main research area is convexity, with particular emphasis on connexions between algebraic and combinatorial properties of convex polytopes.  One significant paper (Inventiones Math 113, 1993, 419-444) contained an elementary proof using notions of decomposition of a central result which classifies the possible numbers of faces of simple polytopes (an important sub-class);  the earlier proof used deep ideas from algebraic geometry.  Another (Discrete Comput Geom 15, 1996, 363-388) further simplified the machinery of that proof to an algebra of (mixed) volumes.

Regular polyhedra have been around since antiquity, and their higher-dimensional analogues have been studied for nearly 150 years.  There are two main thrusts of modern research:  first, construct a suitable abstract theory, and second, classify interesting families of abstract regular polytopes.  A long-standing collaboration with Egon Schulte (Northeastern University, Boston) should soon result in a monograph, Abstract Regular Polytopes.

This page was last modified on September 25, 2009 by Helen Higgins