Nov. 2, 2021

Death of Nessim Sibony

We are saddened to learn of the death of our colleague, Professor Emeritus Nessim Sibony, who once headed the LMO, and also the Harmonic Analysis team.

After important works in Several Complex Variables, holomorphic convexity, positive currents, invariant metrics, and d-bar analysis, Nessim Sibony pivoted to Multidimensional Holomorphic Dynamics, a field that he truly founded in France. His famous collaborations with John Erik Fornaess, and then Tien-Cuong Dinh, punctuated the development of this field with remarkable results. Furthermore, his ex-Ph.D. students --- Vincent Guedj, Charles Favre, Romain Dujardin, Gabriel Vigny --- still work in this area currently.

In the early 1990s, Nessim Sibony deepened our understanding of closed positive currents and of their intersections within the context of complex multivariate dynamical systems. It was a key moment, which led to extraordinary theoretical developments. Today we still rely on these currents to study Julia sets, invariant measures, and many other dynamical objects.

The study of submanifolds of arbitrary dimension and codimension, and more generally, of currents of arbitrary bi-degree (p,p), has always been considered tricky/delicate, particularly because pluripotential theory was not developed for these currents when p > 1. With his collaborators, Nessim Sibony introduced superpotential theory and current density theory, which overcame the underlying difficulties and made it possible to embrace arbitrary dimension and codimension.

More recently, Nessim Sibony applied his geometric currents theory to Riemann surface laminations, developing a beautiful set of theoretical results as for instance: fine ergodic theorems; ergodic uniqueness; and the solutions of the d-bar and Laplacian equations on laminations.

At 74 years of age, Nessim Sibony was still hoping to systematically rework Nevanlinna theory with his new techniques and ideas. Illness prevented him from advancing any further on this great adventure.