Motives, Polylogs, and Non-Abelian Hodge Theory

小行星9801647 该奖项为将在加州尔湾大学举行的关于动机、多元性和霍奇理论的会议提供了支持。20年前，S。布洛赫了他著名的系列讲座理论的difficulms在欧文。这些富有洞察力的讲座奠定了基础的理论相结合格罗滕迪克的理论动机与代数K理论和数论。值得注意的是，每个主题和例子从布洛赫的原始治疗已成为一个活跃的领域，导致新的发现或成长为一个主题本身的权利。 最近出现了两个主要的程序之间的边界地带代数几何，代数K理论和霍奇理论。第一个是代数簇的稳定同伦理论，第二个是非交换的Hodge理论。 20年后是一个很好的时间来回顾和看看领域的立场。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。代数几何是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，它已经有了革命性的发展。在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，在这些领域以及物理学、理论计算机科学和机器人技术中也得到了应用。

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.