MSRI Workshop: May 12 - May 16, 1998 (Berkeley, CA) Title: Homotopy theory for algebraic varieties with applications to K-theory and quadratic forms Abstract: Very recent work of Vladimir Voevodsky and his collaborators has much advanced our knowledge of Galois cohomology and algebraic K-theory. This work involves a global approach to the algebraic geometry of algebraic varieties which entails the development of a suitable homotopy theory. This meeting will offer an exposition of these new techniques and discuss some of the applications to algebraic K-theory and the theory of quadratic forms. Primary speaker: Vladimir Voevodsky, Northwestern Other invited speakers: Michael Hopkins, M.I.T. J. F. Jardine, U. Western Ontario Marc Levine, Northeastern Fabian Morel, C.N.R.S. Alexander Merkurjev, U.C.L.A. Markus Rost, Regensburg Jeff Smith, Purdue Andrei Suslin, Northwestern Organizers: Spencer Bloch and Eric M. Friedlander Further details can be found at the MSRI Web site http://www.msri.org MSRI will have a limited amount of funds avaiable to support additional participants.