Recent Advances in Hodge Theory: Period Domains, Algebraic Cycles, and Arithmetic

霍奇理论的最新进展：周期域、代数环和算术

• 批准号: 1259024
• 负责人: Matthew Kerr
• 金额: $ 2.8万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-05-01 至 2014-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1259024&HistoricalAwards=false
• 关键词: Recent; Advances; Hodge; Theory; Period

A summer school and conference on Hodge theory will be held at the University of British Columbia (Vancouver, Canada) from June 10-20, 2013. This award will support 30 US participants at various stages of their careers. The 24 invited speakers are leading experts in aspects of complex and arithmetic geometry, algebraic cycles, and representation theory, which are in the early stages of a synthesis around the study of period mappings and generalized period domains. The conference will accelerate this process and give graduate students and recent Ph.D.'s an opportunity to enter an emerging discipline.In its simplest form, Hodge theory is the study of periods -- integrals of algebraic differential forms which arise in the study of complex geometry, number theory and physics. Its difficulty and richness arise in part from the non-algebraicity of these integrals. What algebraic structure they do have is recorded by symmetry groups called Mumford-Tate groups, and according to the Hodge conjecture (and its variants) should be explained by the presence of objects called algebraic cycles. The conference will serve to disseminate recent progress on both of these fronts, create new interdisciplinary collaborations, and train the next generation of Hodge theorists.The web site for the conference ishttp://www.pims.math.ca/scientific-event/130610-rahtpdaca

霍奇理论暑期班和会议将于2013年6月10日至20日在不列颠哥伦比亚大学(加拿大温哥华)举行。该奖项将支持30名处于职业生涯不同阶段的美国参与者。被邀请的24位演讲者是复数和算术几何、代数循环和表示理论方面的主要专家，这些方面处于围绕周期映射和广义周期域研究的综合的早期阶段。这次会议将加速这一进程，并为研究生和新近获得博士学位的S提供进入一门新兴学科的机会。霍奇理论最简单的形式是研究周期--在复杂几何、数论和物理研究中出现的代数微分形式的积分。它的难度和丰富性部分源于这些积分的非代数性。它们所具有的代数结构是由称为Mumford-Tate群的对称群记录的，根据Hodge猜想(及其变体)，应该通过称为代数圈的对象的存在来解释。这次会议将有助于传播这两方面的最新进展，创建新的跨学科合作，并培训下一代霍奇理论家。会议的网站为ishttp://www.pims.math.ca/scientific-event/130610-rahtpdaca