Pluripotential theory and complex dynamics in higher dimension – Tien-Cuong Dinh – ICM2018

Analysis and Operator Algebras
Invited Lecture 8.13
Pluripotential theory and complex dynamics in higher dimension
Tien-Cuong Dinh

Abstract: Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.

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