Julian P. Revalski
Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences, Sofia

Title: "Variational composition of a monotone operator and a linear mapping with some applications"

Abstract: In this lecture I will speak about a regularized notion of composition of a monotone operator with a linear mapping. This new concept, called variational composition, can be shown to be maximal monotone in several cases where the usual point-wise composition is not. The two notions coincide, however , whenever the latter is maximal monotone. The utility of the variational composition will be demonstrated by applications to subdifferential calculus and elliptic PDE's with singular coefficients.

And

Tomasz Kaczynski,
Departement de mathematiques et d'informatique
Universite de Sherbrooke

Title: "Computational Homology: Evolution of ideas."

Abstract: The aim of this talk is to give a retrospective of a group research on computing homology of spaces and maps. Our initial motivation came from dynamical systems, namely from the computation of the Conley index of a Poincare map and its use for detection of chaos. However we expect considerably more applications in the future to such problems as, for example, image recognition. The discussed topics include cubical complexes, a reduction algorithm, and the method of multivalued acyclic representations for computing homology of a continuous map.