Applied Analysis Seminar

**Thursday September 19 in CoLab, SFU
**

9:30-11:00

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.