WORKSHOP: Quadratic Forms, Algebraic Groups and Algebraic Cobordism, 26-30 August 2008

Algebra is a general machinery which permits to study mathematical objects of various nature by translating them into objects with formal operations such as multiplication or addition, thus providing a structure that can be studied with a wide range of `algebraic' tools. In a certain sense, algebra therefore plays a similar role in all of mathematics as mathematics itself within the natural sciences. Geometry is another ancient branch of mathematics with its very own methods and tools. It originated in the study of the shapes of objects and their position in space. Often, major progress is achieved when methods from one branch of mathematics are applied to another seemingly unrelated branch. One example is the creation of algebraic geometry --- a powerful theory that allows to study algebraic objects via geometric means and vice versa. Topology studies more or less the same geometric objects but in a much more flexible way, allowing the deformation of shape so that only the most essential features remain. The topological way of thinking has strongly influenced many branches of 20th century mathematics. An important recent development in this context is the creation of a theory called motivic topology which fuses features of topology with those of algebraic geometry. This theory originated in the works of Voevodsky who was awarded the Fields Medal in 2002.The conference focuses on two types of classical algebraic objects: quadratic forms and algebraic groups. The theories of these objects have experienced dramatic progress in recent times due to the novel use of geometric methods. The new techniques from motivic topology turned out to be particularly powerful, allowing to prove many long-standing conjectures and opening up completely new directions of research. One of the crucial tools in this new approach is a theory called algebraic cobordism which draws its inspiration from classical theories in topology. The purpose of this conference is to bring together some of the leading experts from quadratic forms, algebraic groups, algebraic cobordism and other related branches of mathematics, in order to present the state of the art of these theories and to enable interaction between specialists with these different backgrounds. Early career researchers will also have an opportunity to present their contributions to these theories and to benefit from the presence of some of the foremost experts on the subject.