Dirichlet Forms and Related Topics
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Toshihiro Uemura
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Department of Mathematics, Faculty of Engineering Science, Kansai University
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Japan
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Panki Kim
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Department of Mathematical Sciences, Seoul National University
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Korea
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Daniel Lenz
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Institute of Mathematics, Friedrich Schiller University Jena
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Germany
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Introduction:
| | The theory of Dirichlet forms has evolved into a robust framework bridging probabilistic and analytic potential theory, providing essential tools for analysis on non-smooth spaces. This session focuses on recent foundational advances and broad applications across three interconnected areas.
First, we address the analysis of local and non-local operators, with particular attention to heat kernel estimates and regularity theory for integro-differential equations and anomalous diffusion. Topics include the fine properties of transition densities and the behavior of associated jump processes.
Second, we feature the versatility of Dirichlet forms in discrete settings and approximation theory, covering spectral geometry on graphs as well as the numerics of SDEs in finite dimensions. We also explore the convergence of Dirichlet forms, providing a rigorous basis for approximating continuous models by discrete ones.
Finally, the session encompasses (stochastic) homogenization, investigating the effective properties of operators in complex heterogeneous media from both probabilistic and PDE perspectives. We aim to discuss asymptotic behaviors and multiscale problems in random environments.
By integrating these themes, the session aims to deepen the interplay between stochastic analysis and differential equations, fostering collaboration among researchers in these fields.
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