# New Perspectives on the $N$-body Problem (13w5055)

## Organizers

(Università ROMA TRE)

(University of Maryland)

John Mather (Princeton University)

(Università di Torino)

## Description

The Banff International Research Station will host the "New perspectives on the $N$-body problem" workshop from January 13th to January 18th, 2013.

For centuries, the N-body problem of Celestial Mechanics has challenged many generation of mathematicians.
Not only it represents an historical milestone of mathematics, but it is paradigmatic of any complex system of interacting particles.
In its full generality, it can not be neither solved nor simplified in a significant way.
As a dynamical system, it has the fascinating feature of hosting
regular and chaotic regimes and has often inspired the elaboration of new mathematical theories.
Indeed, to be attacked efficiently, it requires a sophisticated mixture of algebraic,
analytical, geometrical, topological and probabilistic techniques.

Main issues concern the existence of regions of stability (regular motions), that of regions featuring
complex dynamics (chaos), and the rules of diffusion from one to another region. Collisions and escape trajectories
play a fundamental role. Another appealing problem is the determination of periodic solutions featuring particular
symmetries in space and time.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).