Dr. Bruce N. Cooperstein

Professor, Mathematics Department
Santa Cruz, California
United States

Focus Areas

Higher Education


Dr. Bruce Cooperstein is Professor of Mathematics at University of California, Santa Cruz. Dr. Cooperstein has over 37 years of teaching experience, serving six years as Provost of College Eight, University of California, Santa Cruz and eight years as Chair of the Department of Mathematics, University of California, Santa Cruz. He has written over fifty research papers in algebra and incidence geometry. Professor Cooperstein’s research covers several areas related to groups of Lie type, finite group theory, Galois geometry and, more generally, incidence geometry. By incidence geometry is meant a pair (P,L) consisting of a set P whose members are called points, and a collection L of distinguished subsets of P whose members are called lines. Projective planes (more generally projective space) and generalized quadrangles are examples. Recently he has become interested in the “embeddings” of such geometries - ways in which these geometries can be modeled by point sets in projective space together with some full projective lines. In particular, he is interested in finding the largest - universal - such embeddings and has achieved results for many of the Lie incidence geometries. A related problem that interests Professor Cooperstein concerns characterizing the maximal external subspaces which do not contain any points of various point sets in finite projective space - so called maximal external flats. Such spaces can be used to construct caps on varieties, error-correcting codes, and other combinatorial objects. Another problem which animates Cooperstein’s interest is the possible non-existence of ovoids on hyperbolic quadric in ten (linear dimensions). Another problem that he has undertaken is the characterization of apartments in the shadow geometries of spherical buildings.