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2017 서울대학교 수리과학부 세미나 



Barycentre problems and geometry of the space of probability measures 

ngHeon Kim (University of British Columbia, Canada ) 
Barycentre is the geometric mean of a distribution on a metric space; it is a point that minimizes its average distance squared to the given distribution. Such a point is highly nonunique in general, though we have uniqueness when the underlying space is the Euclidean space or more generally a space of nonpositive curvature with trivial topology. We consider such a notion from the viewpoint of optimal transport which gives a natural distance structure between probability measures.
This allows us to uniquely interpolate many probability distributions, called the Wasserstein barycentre, as initiated by Agueh and Carlier. It also leads to a uniquely defined canonical barycentre, which is obtained by relaxing the notion of barycentre point to a barycentre measure. We will explain these developments, based on join work with Brendan Pass. 







