Motives were introduced by Grothendieck in an attempt to unify cohomology theories and to reformulate the Weil conjectures. As with other great mathematical ideas, it turned out there are many other reasons for studying motives. The most spectacular recent success of the idea of motives was Voevodsky's proof of the Milnor conjecture for which he received the Fields medal in 2002. There have been several other important applications of motives to problems in algebraic geometry and, as a language, the theory has a much broader impact reaching into algebraic number theory and representation theory via the Langland's program. Furthermore, recent developments indicate connections between motives, periods, and physics. The proposed conference intends to bring together researchers from different areas that use motives. To our knowledge, this is the first conference of this kind.
The theory of motives provides a framework that has proved to be a fundamental tool in clarifying and explaining some of the most difficult unsolved problems in algebraic geometry and mathematical physics. In recent years there has been dramatic progress in this direction and motives have evolved from a largely conjectural theory to a theory that is concrete enough to provide a tool for answering problems. The proposed conference intends to have leading experts speak on their various areas of research emphasizing the connections between different fields. The immense progress in the study of motives and the many interactions of this theory with other branches of mathematics has led to a certain degree of inaccessibility, especially for graduate students and non-specialists. We intend to bridge these gaps by having a number of distinguished speakers give survey talks on different subjects. Last not least, we are planning to provide opportunities for young researchers to present their results.
