Within mathematics, as within science in general, there is a need for greater communication between workers from different research specialties. The purpose of this program is to promote the interaction between two core areas of mathematics—analysis and geometry.
Sophisticated methods have been developed in complex analysis, harmonic analysis, partial differential equations, and other parts of analysis; many of these analytic techniques have found applications in geometry. However, research in analysis is often driven by intrinsic motives rather than by potential applications to other parts of mathematics. Geometers can give analysts new perspectives and focus for their research.
On the other hand, analysts often use ideas and tricks that are well-known to themselves, but mysteries to researchers in other areas; so geometers can benefit from an exchange of ideas with analysts by becoming more familiar with the powerful tools of their field.
Such fruitful interactions should not be left to serendipity. This program is intended to enhance communications between analysts and geometers by focusing on recent developments on the borderline of these subjects.