Summer School in Harmonic Analysis

1 September 2003 - 13 September 2003

Aims

Harmonic Analysis is an extremely vital area of research, with applications to many other areas of Mathematics, such as Partial Differential Equations, Lie Group Theory, Complex Analysis, Probability theory and Number Theory. Fundamental problems in classical Fourier analysis, such as the analysis of oscillatory integrals, almost everywhere convergence and boundedness of classical operators, are receiving strong impulse from recent research. Generalised Calder?n-Zygmund theory and phase space techniques for oscillatory integrals find applications in fundamental problems of non-linear analysis, such as Navier-Stokes equation, or wave phenomena in dispersive equations. The theory of invariant second order elliptic or subelliptic operators on Lie groups provides the crucial models for analysis on sub-Riemannian structures and CR-manifolds. Numerous analytic aspects of representation theory of Lie groups are also naturally related to the other themes. A series of short courses will be offered in the Summer School, covering many of these topics and possibly others. The level of the lectures will be adapted to graduate students and will have a consistent introductory part. The overall program will also be interesting for young reserchers with experience in some area of harmonic analysis.