Conference: Derived Categories of Algebro-Geometric Origin and Integrable Systems

这项提议是为了向参加2010年12月19日至24日在以色列耶路撒冷举行的代数-几何原点和可积系统衍生类别会议的美国与会者提供差旅支持。这次会议是由国际和平协会与Dennis Gaitsgory(哈佛大学)和David Kazhdan(希伯来大学)共同组织的。这次会议的目的是聚集表象理论、代数几何和量子场论边缘相关领域的领先专家，目的是揭示所观察到的联系的本质，并促进每个学科的进展。这次会议将讨论以下主题：1)代数几何和表示论中的跨越墙现象；Kazhdan-Lusztig理论的推广及其与Bridgeland稳定性和量子上同调的关系。2)范畴对偶及其与量子场论的关系：几何朗兰兹对偶、同调镜像对称性。高等范畴结构出现在代数几何、表示论和量子场论中。3)规范理论和刘维尔理论对表象理论提出的新问题。这些主题涵盖了表示理论和代数几何方法在几何和数学物理问题上的最新发展。不同的数学科学研究领域和其他科学领域的相互作用总是激发新的发现。这次研究会议旨在交流数学和物理科学的几个不同领域的研究人员。最近在这些领域的新发现进一步加强了这种相互作用。几位年轻的美国科学家将参加这次会议，这将帮助他们在这些领域确立自己的地位，成为该领域未来的领导者。

This proposal is to provide travel support to US participants to the conference Derived Categories of Algebro-Geometric Origin and Integrable Systems to be held in Jerusalem, Israel, December 19-24, 2010. The conference is organized by the PI together with Dennis Gaitsgory (Harvard) and David Kazhdan (Hebrew University). The purpose of this conference is to bring together leading experts in related directions at the borderline of representation theory, algebraic geometry, and quantum field theory, with the goal of uncovering the nature of observed connections and promoting progress in each of the subjects. This conference will cover the following topics: 1) Wall-crossing phenomenon in algebraic geometry and representation theory; generalizations of Kazhdan-Lusztig theory and their relation to Bridgeland stability and quantum cohomology. 2) Categorical dualities and their relation to quantum field theory: geometric Langlands duality, homological mirror symmetry. Higher categorical structures arising in algebraic geometry, representation theory and quantum field theory. 3) New questions of representation theory coming from gauge theory and Liouville theory. These topics cover recent new development of representation theory and algebraic geometric approach to questions in geometry and mathematical physics.Interactions of different mathematical science research fields and other science areas always stimulate new discoveries. This research conference is to interact researchers in several different areas of mathematical and physical sciences. Recent new discoveries in the fields have further strengthened such interactions. Several young US scientists will participate this conference and it will help them to establish themselves in these fields to be the future leaders in the fields.