We will finish the proof that under GCH, dense ideals cannot exist at successors of singular cardinals.  Then we will outline how to separate the density property from the disjoint refinement property above aleph_1, and note remaining open questions.

In the last few years, a gain in adaptive methods to represent a given signal or image arose in the literature. One of the most used but also less understood is the Empirical Mode Decomposition (EMD). After recalling the main concept and properties of the EMD, I will introduce a new way to build adaptive wavelets aiming to perform the same kind of analysis as the EMD. Those wavelets, called empirical wavelets, are based on the idea of detecting modes of compact support in the Fourier domain. I will provide the formulation to build such wavelets and discuss the most delicate part which is the detection of modes in the Fourier domain. Next, I will show that it possible to extend this concept to existing 2D transforms (tensor approach, Littlewood-Paley, Ridgelets and Curvelets). Finally, I will present preliminary results in the analysis of electroencephalogram signals and give ideas of future investigation both on the theoretical and application sides.

This is a continuation of the previous two talks, where we used large cardinals to get a normal, lambda-dense ideal on [lambda]^<kappa, where kappa is the successor of a regular cardinal, and GCH holds near kappa.  In this talk we show that the analogous statement for a successor of a singular cardinal is inconsistent.  If time permits, we will begin discussion of consistently separating certain properties at kappa>omega_1 that coincide at omega_1.