# Currents, their intersection and applications

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Lucas Kaufmann

created by daniele on 10 Dec 2020

modified on 27 Jan 2021

4 feb 2021
-- 14:30

DIMaI, Firenze (online)

Seminario di Geometria Differenziale e Analisi Complessa del Dipartimento di Matematica e Informatica "Ulisse Dini" dell'UniversitĂ di Firenze

**Abstract.**

Positive closed currents are central objects in pluripotential theory and modern complex analysis. They generalize both smooth differential forms and subvarieties. Given two currents it is of central importance to understand when a meaningful notion of intersection (or wedge product) between them can be given. This is useful for instance in producing invariant measures for dynamical systems and in the study of the complex Monge-AmpĂ¨re equation with singular data.

In this talk I aim to overview some basic facts about currents in complex analysis (including their definition) and recent approaches to their intersection theory. I'll also mention some applications to geometry and to the dynamics of maps and foliations.