Motives, Polylogs, and Non-Abelian Hodge Theory

9801647卡扎尔科夫该奖项为在加州大学欧文分校举办的动机、多对数和霍奇理论会议提供支持。20年前，S·布洛赫在欧文发表了关于双对数理论的著名系列演讲。这些富有洞察力的讲座奠定了将格罗森迪克的动机理论与代数K理论和数论相结合的理论基础。值得注意的是，布洛赫最初治疗的每个主题和例子都已经成为一个活跃的领域，导致新的发现或本身成长为一个主题。最近在代数几何、代数K理论和Hodge理论之间的边界地带出现了两个主要的程序。第一种是代数簇的稳定同伦理论，第二种是非阿贝尔Hodge理论。二十年后是回首往事，看看田野是什么样子的好时机。通过聚集所有这些领域的研究人员，组织者希望激发一种创造性的氛围，这将导致许多新的令人兴奋的发现。这次会议是在代数几何领域举行的。代数几何是现代数学中最古老的部分之一，但在过去的25年里，它已经取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。

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.