International Workshop in Complex and CR Geometry, Partial Differential Equations and Invariant Theory

复数和CR几何、偏微分方程和不变量理论国际研讨会

• 批准号: 0635721
• 负责人: David Tartakoff
• 金额: $ 3万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-04-01 至 2009-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0635721&HistoricalAwards=false
• 关键词: International; Workshop; Complex; CR; Geometry

This U.S.-Czech mathematics workshop with mini-courses will bring together a group of pioneering mathematicians who will interact with graduate and post doctoral students to examine approaches for improving accuracy in models for mathematical physics. Organizers, David Tartakoff of the University of Illinois-Chicago and Czech partner, Vladimir Soucek of Charles University, will direct a four-day program of expert lectures and interactive sessions to investigate Cauchy-Riemann (CR) geometry, sometimes called complex-real geometry, suggesting real submanifolds of complex spaces. Invited U.S. participants include M.S. Baouendi, J. J. Kohn, L. Lempert and Y.-T. Siu. Among the invited Europeans are leading Czech mathematicians, M. Bures, M. Englis, M. Kolar and J. Slovak. With a goal of developing general systems for partial differential equations, the workshop agenda is designed to integrate current discussions on key unsolved problems while exposing junior workshop participants to an emerging branch of mathematics.The envisioned interaction should benefit from U.S. expertise in CR geometry, partial differential equations and analytic methods in complex algebraic geometry. Similarly, the Czechs will contribute complementary strengths in parabolic geometry and invariant differential operators on manifolds. One important workshop objective is to explore links between invariant differential operators and the generalized Bernstein-Gelfand-Gelfand (BGG) complexes and curved versions. Results from this and other exchanges are expected to help define mathematically accurate models for complex analysis, mapping and geometry problems. This workshop fulfills the program objective of advancing scientific knowledge by enabling experts in the United States, the Czech Republic, and other European countries to combine complementary talents and share research resources in areas of strong mutual interest and competence. Broader impacts include early career introduction of U.S. graduate and post doctoral students to leading theorists and mathematicians in the European research community.

这个美国-捷克数学研讨会与迷你课程将汇集一批开拓数学家谁将与研究生和博士后学生互动，研究提高数学物理模型的准确性的方法。 组织者，伊利诺伊大学芝加哥分校的大卫塔尔塔科夫和捷克合作伙伴，查尔斯大学的弗拉基米尔苏切克，将指导为期四天的专家讲座和互动会议计划，以研究柯西-黎曼（CR）几何，有时称为复杂的真实的几何，提出复杂空间的真实的子流形。 受邀的美国与会者包括M. S。Baouendi，J. J. Kohn，L. Lempert和Y. T.萧 受邀的欧洲人中有捷克著名数学家M. Bures，M. Englis，M. Kolar和J. Slovak. 以发展偏微分方程的一般系统为目标，讲习班的议程旨在整合当前对关键未解决问题的讨论，同时使初级讲习班参与者接触到一个新兴的数学分支。设想的互动应受益于美国在CR几何、偏微分方程和复代数几何分析方法方面的专业知识。 同样，捷克人将在抛物几何和流形上的不变微分算子方面贡献互补的力量。 研讨会的一个重要目标是探索不变微分算子与广义Bernstein-Gelfand-Gelfand（BGG）复形和弯曲版本之间的联系。 从这个和其他交流的结果，预计将有助于定义数学上准确的模型，复杂的分析，映射和几何问题。该研讨会通过使美国，捷克共和国和其他欧洲国家的专家能够联合收割机互补人才和共享具有强烈共同兴趣和能力的领域的研究资源来实现推进科学知识的计划目标。 更广泛的影响包括美国研究生和博士后学生的早期职业介绍给欧洲研究界的领先理论家和数学家。