XXXVIII Workshop on Geometric Methods in Physics | 30.06-6.07.2019 |

VIII School on Geometry and Physics | 24-28.06.2019 |

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## Jimmie Lawson## The Road to the Operator Geometric Mean with Stops Along the WayWe 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. |

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University of Bialystok |

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