Workshop Travel to Study Analysis and Geometry in Metric Spaces

Kenyon College, Gambier OH

Investigators

Abstract

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/