Study of convergence and collapsing phenomena by methods of geometric analysis

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We obtained the uniqueness and the stability of the inverse spectral problemconcerning the local data of the heat kernels in the moduli of closed Rimennian manifolds whose sectional curvature and diameters are uniformly bounded (T.Yamaguchi, S. Kurylev, M.Lassas). We classified the collapsing phenomena of three-dimensional closed Alexandrov spaces with cuvature uniformly bounded below. Moreover we proved the local strong Lipschitz contractibility of Alexandrov spaces and the stability of strongly Lipschitz contractible balls(T.Yamaguchi, A.Mitsuishi). We proved that the curvature dimension condition of Ricci curvature is preserved under the concentration of metric measure spaces(T.Shioya, K.Funano). We reconstructed hyperbolic orbifolds from S-matirix corresponding to a general end (H. Isozaki, Y. Kurylev).