XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019
VIII School on Geometry and Physics 24-28.06.2019

Jimmie Lawson

The Road to the Operator Geometric Mean with Stops Along the Way

We trace the path of development of the matrix and operator geometric mean from its beginnings
as a two-variable mean to a multi-variable mean and barycentric map on integrable measures
on the cone of positive elements of an arbitrary unital $C^*$-algebra. We point out a variety of major mathematical tools and theories, primarily geometric ones, that have been crucial at varying stages
to make possible these developments: the theory and stochastics of non-positively curved (CAT_0)
metric spaces, Riemannian geometry, the Thompson metric, a new class of power means, and the Wasserstein metric on probability measures, to mention some of the key ones.

Event sponsored by:
of Bialystok
University of Bialystok

Webpage by: Tomasz GolinskiTomasz Golinski