The impact of geometric flows and metric analysis, e.g., in the form of Gromov-Hausdorff limits, represent some of the most dramatic recent developments in geometry in the large. When combined, this has resulted in the spectacular resolution of the famous Poincare and geometrization conjectures. The main objectives of the workshop on Interactions between Geometry and Analysis to be held at Notre Dame, October 21-24, 2010 is to facilitate further interactions between geometry and analysis at the level of cutting edge research, and to secure long term gains by involving students and post docs in the process.
Geometry and Analysis are both highly developed and vast subjects in mathematics, with numerous important applications to other areas of mathematics, to physics, economics and engineering. Although interactions between these subjects also has a significant and even profound history, recent developments involving flows and limit space objects has propelled this evolution in a significant way both in terms of spectacular results already achieved as well as opening up future promising directions of research. The 4-day workshop on Interactions between Geometry and Analysis to be held at Notre Dame University will bring together some of the leading experts in these areas and provide a setting in which these researchers will naturally interact with one another as well as with graduate students and young post docs.
propelled by recent advances in various directions including applications of geometric flows and analysis of and via metric spaces, i.e., spaces equipped with a notion of distance. The format consisted of presentations of cutting edge research by twelve experts in the two general areas of focus, allowing time for questions, discussions and interactions during and after the presentations. In addition, space was made available for such activities, and a successful general "brain storm session" was organized. In addition to promoting research activities in geometric analysis and related areas in the mid-west region, it was a special goal for the workshop to provide an informal setting where graduate students and younger researchers would learn of the newest trends and interact with some of the most prominent geometers around the world. The workshop attracted more than twice the number of participants originally planned and budgeted for, and well over half of them were graduate students or young post docs. from across the US and even abroad. It is apparent from those involved that our goals were fully met, and that many new contacts were established providing a bases for promising future developments.
