Motives, Polylogs, and Non-Abelian Hodge Theory

9801647 Katzarkov这个奖项为将在加州大学欧文分校举行的关于动机、多对数和霍奇理论的会议提供了支持。20年前，S. Bloch在欧文做了著名的二重算术理论系列讲座。这些富有洞察力的演讲奠定了格罗滕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，布洛赫最初的治疗方法中的每个主题和例子都成为一个活跃的领域，导致新的发现或发展成为自己的主题。最近在代数几何的边界地带出现了两个主要的程序，代数k理论和霍奇理论。第一种是代数变异的稳定同伦理论，第二种是非阿贝尔霍奇理论。二十年后是回顾过去的好时机。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，从而产生许多令人兴奋的新发现。这次会议的主题是代数几何。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。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它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.