Geodesics

August 23 to August 27, 2010

at the

American Institute of Mathematics, San Jose, California

organized by

Victor Bangert and Yiming Long

Original Announcement

This workshop will be devoted to the study of the behavior of geodesics in the large. Although this is an old subject, with important contributions first made by J. Hadamard and H. Poincare, many of the fundamental problems are still open.

The study of geodesics is a central part of Riemannian geometry, of the calculus of variations and of Hamiltonian dynamics. Beyond that it is related to a remarkably large number of mathematical and non-mathematical fields ranging from the study of PDEs to number theory and from transport problems to general relativity. So it is no surprise that often progress in geodesic problems is achieved by combining ideas and methods from different areas.

The workshop will stimulate exchange and cooperation between researchers from diverse mathematical fields with interest in geodesics.

Here is a non-exhaustive list of topics to be discussed in the workshop.

Morse theory on loop spaces.
Statistical properties of geodesic flows, dynamical zeta-function.
Rigidity and geodesics.
Symplectic geometry and J-holomorphic curves applied to geodesics.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Open problems and questions about geodesics

by Keith Burns and Vladimir S. Matveev

Resonance for loop homology of spheres

by Nancy Hingston and Hans-Bert Rademacher, J. Differential Geom. 93 (2013), no. 1, 133-174 MR3019513