I research the convergence theory of Riemannian manifolds and metric measure spaces. More specifically, I study the convergence of such spaces and the geometric analytic properties of convergent sequences of spaces and of their limit spaces. In particular, I am interested in the concentration topology (on the set of all metric measure spaces) based on the concentration of measure phenomenon. This topology is effective to capture the high-dimensional aspects of spaces, and indeed infinite-dimensional spaces appear as the limit spaces.

Keywords	Geometric analysis, Metric measure space, Convergence theory
Faculty , Department	Faculty of Mathematics , Division of Algebra and Geometry