9801647 Katzarkov This award provides support for a conference on motives, polylogarithms, and Hodge theory to be held at the University of California Irvine. Twenty years ago, S. Bloch gave his famous lecture series on the theory of dilogarithms in Irvine. These insightful lectures laid the foundation of a theory that combined Grothendieck's theory of motives with algebraic K-theory and number theory. Remarkably, each topic and example from Bloch's original treatment has become an active area leading to new discoveries or growing into a subject in its own right. Two major programs have recently emerged in the boundary zone between algebraic geometry, algebraic K-theory and Hodge theory. The first is stable homotopy theory of algebraic varieties, and the second is non-abelian Hodge theory. Twenty years later is a good time to look back and see where the fields stand. By gathering researchers in all of these fields, the organizers hope to stimulate a creative atmosphere that will lead to many new exciting discoveries. This conference is in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.
