17:00
Currents in metric spaces, isoperimetric inequalities, and applications to area minimization problems
Abstract
Integral currents were introduced by H. Federer and W. H. Fleming in 1960
as a suitable generalization of surfaces in connection with the study of area
minimization problems in Euclidean space. L. Ambrosio and B. Kirchheim have
recently extended the theory of currents to arbitrary metric spaces. The new
theory provides a suitable framework to formulate and study area minimization
and isoperimetric problems in metric spaces.
The aim of the talk is to discuss such problems for Banach spaces and for
spaces with an upper curvature bound in the sense of Alexandrov. We present
some techniques which lead to isoperimetric inequalities, solutions to
Plateau's problem, and to other results such as the equivalence of flat and
weak convergence for integral currents.
17:00
From Dutch dykes to value-at-risk: extreme value theory and copulae as risk management tools(Nomura Lecture)
Abstract
In Clarendon Lab