ABSTRACT Modern celestial mechanics starts with Isaac Newton’s Principiain 1687. • Already Poincaré (1854–1912) had observed that a system ofseveral celestial bodies moving under Newton’s gravitational law shows chaoticdynamics. • Even earlier, Euler and Lagrange had found areas where themotion seems to be more stable. The subtle interaction between stability andchaos leads to interesting dynamical phenomena. A spacecraft in thegravitational fields of the sun, the earth, and the moon provides an interestingsystem of this kind. The mathematical problems arising from celestial mechanicshave led to many mathematical theories.Among these there is a geometry, where thebasic concept is area and not distance.Many conservative dynamical systems arecompatible with this geometry and this facthas many striking consequences. In thislecture, having a general mathematicalaudience in mind, the basic ideas andconsequences are described in a non-technical manner.

PDEs and Fractals • Geometry with its applications has been at the heart ofthe development of partial differential equations and boundary value problems since the verybeginning. In physics, biology, economics, and other applied fields, a variety of new problemsare now emerging that display unusual geometrical, analytical and scaling features, possiblyof fractal type. The objective of these lectures is to acquire the view of outstanding mathemati-cians on the subject of differential equations and fractals, and their developments and applica-tions, in a broad perspective encompassing both classical highlights and contemporary trends.

Sponsored by WPI and hosted by the Department of Mathematical Sciences

Refreshments available before the lecture • Participation of faculty and students is most welcome

wpi.edu/+hgayPoster Organization: Rhonda Podell

Helmut HoferInstitute for Advanced Study, Princeton

A Geometry Based on Area and Dynamical SystemsFriday, March 25, 2016 3:00pm, Higgins Labs 218

H A R O L D J G A YLECTURE SERIES

This talk has been postponed;

it will be rescheduled for a

later date (to be determined).