Stochastic and geometric analysis on manifolds and metric measure spaces
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Kazuhiro Kuwae
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Fukuoka University
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Japan
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Xiangdong Li
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Chinese Academy of Sciences
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Peoples Rep of China
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Asuka Takatsu
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University of Tokyo
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Japan
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Introduction:
| | Since the middle of 1970s, stochastic geometric analysis has achieved a great success in the mathematics research, for examples, the probabilistic proof of the H\"ormander hypoellipticity theorem, the probabilistic proof of the Atiyah-Singer index theorem of the Dirac operator, and stochastic analysis and geometry on path and loop spaces. During the last thirty years, the optimal transportation theory, in particular, the gradient flow theory on the Wasserstein space of probability measures, has provided a new insight to study various problems in the Monge-Ampere equation, geometric PDEs, fluid hydrodynamics and has important applications in statistical mechanics and information theory. More recently, inspired by the works of M. Gromov, S. Amari and F. Otto, J. Lott, K.T. Sturm and C. Villani have developed the synthetic geometric analysis on metric measure space with curvature-dimension condition. Furthermore, progress is being made not only in spaces with Riemannian structures but also in spaces grounded in Lorentzian structures and in generalizations based on sub-Riemannian structures. In light of this current state, this session will feature talks by a wide range of leading researchers in manifolds, measure-metric spaces, and applications in image processing, aiming to promote cross-disciplinary advancement in this field.
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