Special Meeting: Focus Program on Whitney Problems

该奖项提供支持，以支付“特别会议：关注惠特尼问题的方案”的美国与会者的费用。该计划将包括三项活动(为期7天的研讨会、研究生课程和系列讲座)，将于2012年8月27日至9月3日在加拿大多伦多的菲尔兹数学科学研究所举行。特别会议的重点是函数论中与著名的惠特尼延拓和光滑函数类的迹问题有关的一些最活跃的发展。这些领域包括研究有限集上的Lipschitz结构的新的解析和几何方法，Sobolev空间中函数的延拓和迹问题，从度量空间的子集同时延拓Lipschitz函数，Helly-型Lipschitz选择问题，Sobolev延伸域的几何描述等。这些领域的新发展将继续对包括函数论、几何分析和复杂性在内的广泛领域产生影响。美国国家科学基金会为这项计划提供的资金将用于支付美国参与者支持的费用，优先考虑研究生、博士后、年轻教师、未被充分代表的群体成员和没有自己资金来源的人。本课程将汇集分析、偏微分方程式、几何学的研究人员，讨论与惠特尼问题有关的最新进展，特别是这些数学领域之间的重叠。该计划将有机会吸引一些在函数论、偏微分方程式和调和分析方面的顶尖专家一起讨论这个问题和相关的感兴趣的研究问题。该计划将创造一个环境，让学生和早期职业研究人员可以从与这些顶尖专家的互动中受益。

The award provides support to defray the expenses of US participants in the "Special Meeting: Focus Program on Whitney Problems". The program will consist of three activities (a 7-day workshop; a graduate course; and a lecture series) that will take place August 27 through September 3, 2012, at the Fields Institute for Research in the Mathematical Sciences in Toronto (Canada). The special meeting is focused on some of the most vibrant developments in function theory related to the celebrated Whitney extension and trace problems for classes of smooth functions. These include new analytic and geometric methods in the study of Lipschitz structures on finite sets, extension and trace problems for functions in Sobolev spaces, simultaneous extensions of Lipschitz functions from subsets of metric spaces, Helly-type Lipschitz selection problems, geometric descriptions of Sobolev extension domains, etc. New developments in these areas will continue to have an impact on a broad range of fields, including function theory, geometric analysis and complexity.NSF funding for this program will be used to pay for the expenses of US based participant support, with priority given to graduate students, post-docs, younger faculty, members of underrepresented groups, and those without their own source of funding. This program will bring together researchers in Analysis, Partial Differential Equations, Geometry,to discuss recent advances related to the Whitney Problem and in particular the overlap between these areas of mathematics. The program will be an opportunity to attract some of the leading experts in function theory, partial differential equations, and harmonic analysis together to discuss this question and related research questions of interest. This program will create an environment in which students and early career researchers could profit from the interaction with such top experts.