Support for US Participants at CIRM, March 13-17, 2017 Conference: Scattering, Resonances and Dynamics

University Of Oklahoma Norman Campus, Norman OK

Investigators

Abstract

The workshop "Resonances: Geometric Scattering and Dynamics," taking place at the Centre International de Recontres Mathématiques (CIRM) in Luminy, France, from March 13 to 17, will gather researchers working on the different aspects of the geometric theory of resonances (spectral geometry, representation theory, harmonic analysis, microlocal analysis, analytic number theory, mathematical physics, microlocal analysis, quantum dynamics, geometric scattering theory) as well as Ph. D. students and junior researchers from different countries. Its objectives are to present and discuss the latest results on the geometric aspects and dynamics of resonances, share points of view and ideas, and to strengthen or promote interactions. The conference will give Ph.D. students and young scientists the opportunity to meet some of the prominent researchers in the fields related to resonances and to exchange ideas with them. To make the more specialized talks accessible to the participants, some experts will give tutorial and survey talks. Moreover, two afternoons will be devoted to talks of junior participants. This will give the Ph.D. students and the postdocs the possibility of presenting their work, which is an essential step for entering in the world of research and for building scientific collaborations. The notion of resonance was introduced in quantum mechanics to study metastable states of a system, that is long-lived states from which the system deviates only with sufficiently strong disturbances. Mathematically, resonances appear either as discrete eigenvalues of the quantization of a classical Hamiltonian or as the eigenvalues of the transfer operator of the classical flow. Their study, initially aimed at Schroedinger operators on R^n, was extended to more geometric situations. Because of the role they play in various physical contexts there has been a considerable progress in understanding the geometry and the analysis of classical and quantum resonances in the last years. Nevertheless, many important and basic questions are still open. Many difficulties preventing to use classical arguments arise because of the non-self-adjoint nature of resonances. Also, in the geometric case of (locally) symmetric spaces, very little is known when the rank of the spaces is bigger than 1. Partial advances have been obtained, with several different approaches, using either harmonic analysis and representation theory, or microlocal analysis and techniques from scattering theory such as complex scaling. To study resonances in higher dimensional and higher rank geometric situations, a joint effort of different mathematical communities is therefore needed, and young researchers should have contacts with experts from the various aspects of the theory to make significant progress. The webpage listing of the conference: http://scientific-events.weebly.com/1604.html