Stéphane Jaffard: New directions in multifractal analysis

Multifractal analysis deals with the estimation of the Haudroff dimensions of the sets of points where the pointwise regularity exponent of a function (or a measure) takes a given value. It has both theoretical aspects (the determination of this ``multifractal spectra'' (in deterministic or random settings) having lead to new techniques for computing Hausdorff dimensions) and applied aspects, through the ``multifractal formalism'' which yields an estimate of the multifractal spectrum via quantities which are effectiveley computable for real-life data, and lead to signal or image classification tools. We will show how this subject has recently evolved through the introduction of new regularity exponents and ``second generation exponents'' which give a finer description of the behavior of the function near a singularity.