~ ABSTRACT ~

 

Analysis, Models and Simulations
Pierre-Louis Lions, Collège de France and École Polytechnique

In this talk, we shall first present several examples of numerical simulations of complex industrial systems. All these simulations rely upon some mathematical models involving Partial Differential Equations and we shall briefly explain the nature, the history and the role of such equations. Then, some examples showing the importance of the mathematical analysis (i.e. "understanding") of those models will be presented. And we shall conclude indicating a few trends and perspectives.

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A New Method for Approximations in Probability and Operator Theories
Vidmantas Bentkus, Vilnius Pedagogical University

The aim of the lecture is to introduce a new approach in normal approximations, approximations of semigroups of operators, and approximations by accompanying laws. We describe the method and provide examples showing how the method works. Loosely speaking, the approach is based on multiplicative representations of differences to estimate. The method reduces considerably the technical part of proofs compared to the traditional approaches. In probability it applies nicely to the non-identically distributed case; another advantage of the method is its extendibility to the case of dependent random variables. Current research results using the method will be discussed.

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Statistics of Extremes
Jef L. Teugels, Katholieke Universiteit Leuven & EURANDOM

Extreme value theory is gradually becoming part of standard statistical knowledge. The unifying approach that has been developed over the last decades has clearly indicated that both theory and practice of extreme value methodology have matured. We will survey the most important aspects of the theory. To illustrate the theoretical results we give a number of applications from insurance and geology.

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