Fractional dimensions of critical loci (Maxim KONTSEVICH, IHES Paris)

25.09.2025 16:15

With a critical locus of a holomorphic function, one can associate a certain rational number that can be thought of as a "dimension." This dimension can be determined in different ways: via analysis, Hodge theory, or triangulated categories. Singularities with a dimension less than one are precisely the isolated simple ones classified by Arnold, which correspond to the simply laced Dynkin diagrams


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