Entropy of autoequivalences and holomorphicity

Abstract: The notion of entropy of an endofunctor categorifies the notion of topological entropy of a continuous map. However, while the latter is a number, the former is a function of a real variable. The value at zero of this function takes the name of categorical entropy and makes the connection between the categorical and the topological framework. In this talk I will report on joint work with Jongmyeong Kim in which we give sufficient conditions for a conjecture in categorical dynamics (that mirrors a theorem of Gromov and Yomdin) to be satisfied. Of particular interest is the fact that such conditions arise, through the philosophy of homological mirror symmetry, as a categorification of one of the properties of holomorphic functions.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

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