Workshop Travel to Study Analysis and Geometry in Metric Spaces

该奖项将为16名美国数学家提供支持，以参加2015年4月至6月在西班牙马德里的数学科学研究所（ICMAT）举行的度量空间分析和几何研究学期。 度量空间是有用的模型，任何时候都可以考虑具有自然“距离”概念的对象集-例如，图像，DNA序列和数据一般都可以用度量空间建模。 在度量空间中发展微积分是有用的，部分原因是它允许人们在这些设置中制定和解决优化问题。这个研究术语将，特别是，集成度量空间理论与各种各样的应用，包括图像处理，重建理论，控制理论和机器人技术。更具体地说，程序汇集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，以及度量测度空间上的有界变差函数），几何测度论和变分问题（特别是在次黎曼设置），以及弱曲率的版本（例如，亚历山德罗夫空间的设置）。 预计它将促进这些领域之间的思想和技术的交流，并建立研究人员之间的国际合作。时间表包括四个为期一周的小型课程，由度量空间分析和几何方面的领先专家在5月份为非专业人士和年轻研究人员授课，随后在6月份举办了一个研讨会，汇集了小型课程的主题。 该奖项将优先为研究生、早期职业数学家和来自代表性不足群体的数学家提供旅行支持。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/