Victor Pambuccian completed his doctorate in 1993 at the University of Michigan, with a thesis focusing on the axiomatics of Euclidean geometry, under the guidance of advisor Andreas Blass. He came to Arizona State University in 1994.
Pambuccian’s wide-ranging research interests include the axiomatics of a variety of geometries, such as affine, projective, Euclidean, ordered, equiaffine, hyperbolic and the geometry of metric planes. He also examines definability questions in several geometries, including Minkowski space. Another interest focuses on reverse geometry, which is the search for the most austere axiom systems inside which a certain theorem can be proved.
A prolific author, Pambuccian has written 100 journal publications. Recent examples include “The axiomatics of ordered geometry I. Ordered incidence spaces” in Expositiones Mathematicae, “Axiomatizing geometric constructions” in Journal of Applied Logic (he also serves on the editorial board of this publication), and “The Erdös-Mordell inequality is equivalent to non-positive curvature” in Journal of Geometry.
Currently, Pambuccian is writing a book about the axiomatic foundation of geometry, which will survey all contributions made from the 1882 beginning of the modern axiomatization of geometry to the present.