Workshop Travel to Study Analysis and Geometry in Metric Spaces

该奖项将支持16名美国数学家参加2015年4月至6月在西班牙马德里的圣马蒂卡斯学院(ICMAT)举行的米制空间分析与几何研究学期。度量空间在任何时候都是有用的模型，只要您想要考虑具有自然的“距离”概念的对象集--例如，图像、DNA序列和一般数据都可以用度量空间建模。在度量空间中开发微积分在一定程度上是有用的，因为它允许人们在这些环境中制定和解决优化问题。这一研究术语将特别将度量空间理论与图像处理、重构理论、控制理论和机器人等广泛的应用相结合。更具体地说，该程序集合了度量空间研究的三个领域：一阶分析(包括Sobolev空间的理论、p-Laplace方程的解和度量度量空间上的有界变差函数)、几何度量理论和变分问题(特别是在次黎曼环境下)以及弱曲率的形式(例如Alexandrov空间的设置)。预计它将促进这些领域之间的思想和技术的交叉交流，并在研究人员之间建立国际合作。课程安排包括在5月份为非专业人员和年轻研究人员讲授四门为期一周的迷你课程，由米制空间分析和几何方面的领先专家授课，随后在6月份举行研讨会，汇集迷你课程的主题。该奖项将优先支持研究生、职业生涯初期的数学家和来自代表性不足群体的数学家。研究术语网站：http://www.icmat.es/RT/AGMS2015/

This award will provide support for sixteen U.S. mathematicians to participate in the Research Term on Analysis and Geometry in Metric Spaces from April through June, 2015 at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid, Spain. Metric spaces are useful models anytime one wants to consider sets of objects with a natural notion of "distance" -- for example, images, DNA sequences, and data in general can be modeled with metric spaces. Developing calculus in metric spaces is useful in part because it allows one to formulate and solve optimization problems in these settings. This research term will, in particular, integrate metric space theory with a wide variety of applications including image processing, reconstruction theory, control theory, and robotics.More specifically, program brings together three areas of metric space research: first-order analysis (including theories of Sobolev spaces, solutions to the p-Laplace equation, and functions of bounded variation on metric measure spaces), geometric measure theory and variational problems (particularly in the sub-Riemannian setting), and versions of weak curvature (for example, the the setting of Alexandrov spaces). It is expected to facilitate crossflow of ideas and techniques between these areas and establish international collaborations between researchers. The schedule includes four, week-long minicourses for non-specialists and young researchers during the month of May taught by leading experts in metric space analysis and geometry, followed by a workshop in June that brings together topics from the minicourses. Priority for travel support from this award will be given to graduate students, early-career mathematicians, and mathematicians from under-represented groups.Research Term web site: http://www.icmat.es/RT/AGMS2015/