- Elementary Geometry from an Advanced Point of View
- NOMA’11: International Workshop on Nonlinear Maps and their Applications
- Intelligent Data Analysis Analyzing and Understanding Complex Systems

The use of wavelet analysis is very common in a large variety of disciplines, such as signal and image processing, quantum mechanics, geophysics, medicine, biology, etc. In economics, however, wavelets are still a mysterious, but colorful, tool for time-series analysis. 

In the diverse geoscience problems investigated at the Instituto Dom Luiz (IDL), a partner of CIM, the iden- tification and quantification of trends is one of the most ubiquitous activities. From the analysis of the outputs of complex meteorological numerical models in a climate change context to the exploitation of geophysical re- sources and renewal energy sources, accurate knowledge of trends and corresponding uncertainties is fundamen- tal for answering most scientific and societal questions.

Research in many areas of the Geosciences is pursued at Instituto Dom Luiz (IDL), an Associated Laboratory of the University of Lisbon that is a partner of CIM. In the Atmospheric and Climate Modelling group at IDL, research on basic fluid dynamics relevant to meteorology is carried out, using numerical and analytical methods. As a member of this research group with a particular interest in analytical and semi-analytical mathematical techniques, the author will try to describe in this paper some aspects of research on mountain waves, which is perhaps one of the most interesting areas from an applied mathematics point of view.

The various nature of the mathematical objects in what concerns their complexity, our knowledge of them or the possibility to make them explicit (for example, infinitesimal or ilimited real numbers) is a strong motivation to consider their distribution into levels or strata. The stratification depends on the selected property (or properties) of the mathematical objects that are the subject-matter of our study

In 2000 the World Mathematical Year offered an occasion for a collective reflection on the great challenges of the 21st Century, on the role of Mathematics as a key for the development and on the importance of the image of Mathematics in the public understanding. The countless repeated phrase “the Universe is written in mathematics language”, written by Galileu in 1614, is truer than ever but it raises new challenges in the current age of data-intensive science driven, in particular, by the information and communication technologies. The “rising tide of scientific data” created by the digital revolution provides new possibilities to face some of society’s great challenges of energy and water supply, global warming and healthcare

A Planet to discover: oceans; meteorology and climate; mantle processes, natural resources; celestial mechanics; cartography.