During the 1980's the closely related subjects of the algebraic theory of quadratic forms and the theory of finite- dimensional division algebras benefitted greatly from developments in algebraic K-theory and algebraic geometry. The topics of this conference, historically speaking, are rooted in number theory. Most of the main problems and motivation have number theoretic origins. In the first half of this century, these subjects blossomed with the development of modern algebraic number theory. The discovery of local-global principles for quadratic forms was bound up with the development of p-adic fields. Further, the classification of finite-dimensional division algebras over local and global fields was closely connected to the development of class field theory. In the past forty years, each of these subjects has declared much independence from number theory. This project will support the 1992 Summer Research Institute on Quadratic Forms and Division Algebras: Connections with Algebraic K-theory and Algebraic Geometry (the fortieth in the series) to be held from July 6 - 24, 1992 at the University of California, Santa Barbara. The primary topics of the summer institute are the closely related subjects of finite-dimensional division algebras and the algebraic theory of quadratic forms. Further progress is expected to be stimulated by holding two special lecture series, one devoted to algebraic K-theory and the other to algebraic geometry. In addition, there will be research lectures on the two principal themes, quadratic forms and division algebras. The first week of the institute will have quadratic forms emphasis, the third week will have division algebra emphasis, and the second week will emphasize both with the hope of stimulating interaction.
