Oakes Faculty Fellows

The Oakes College faculty represents a wealth of expertise from the natural sciences to the humanities, and we are proud to have some of the top scholars in the world among our faculty. Our students major in nearly every discipline at UCSC—from economics and computer science, to theater arts and Latin American and Latino studies—and they are well supported by the depth and breadth of the Oakes College faculty and the extensive knowledge of our advising team.

TBA is Oakes's faculty chair!

The Chair of the Faculty is an Academic Senate member, other than the Provost, who is elected by the college Faculty to serve a two year term, and will serve as a member of the Executive Committee.

 

Bruce Cooperstein
  • Title
    • Distinguished Professor
  • Division Physical & Biological Sciences
  • Department
    • Mathematics Department
  • Phone
    831-459-2150
  • Email
  • Fax
    831-459-4511
  • Website
  • Office Location
    • McHenry Library, McHenry Building #4157
  • Mail Stop Mathematics Department
  • Mailing Address
    • 1156 High Street
    • Santa Cruz CA 95064

Research Interests

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.

Biography, Education and Training

B.A. Queens College, City University of New York
M.A., Ph.D., University of Michigan

Selected Publications

  • B. Cooperstein: (With A. Cohen): Lie Incidence Systems viewed as Intersections of Quadrics. Proceedings of the American Mathematical Society, volume 126, number 7 (July 1998), 2095-2102.
  • B. Cooperstein: On a Connection Between Hyperbolic Ovoids on the Hyperbolic Quadric Q (10,q) and the Lie Incidence Geometry E6,1(q), 55-64 in Groups and Geometries, Birkhauser, 1998.
  • B. Cooperstein: On the Generation of Dual Polar Spaces of Unitary Type Over Finite Fields. European Journal of Combinatorics 18 (1997), no.8, 849-856.
  • B. Cooperstein: External Flats to Varieties in PG(Mn,n(GF(q)). Linear Algebra and Its Applications, 267 (1997), 175-186.
  • B. Cooperstein: On the Generation of Some Dual Near Polygons of Symplectic Type Over GF(2). European Journal of Combinatorics 18 (1997), no. 7, 741-749.