# Regular Faculty

**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.