AbstractIn this talk, we explain the classificatin of the metric fibration that is a metric analogue of topological fibration introduced by T. Leinster in the study of magnitude. The magnitude of metric spaces, also introduced by Leinster, is an analogy of the Euler characteristic from a viewpoint of enriched category theory. As the Euler characteristic of the usual fibration splits into those ...
Abstract:We first give an brief introduction on the topic of hyperplane arrangement. Then we give concrete formulas for these L^2 type invariants at degree 1 and study their connections with combinatorics. If time allows, some similar results for smooth complex quasi-projective variety will be discussed