## THE ABEL SYMPOSIUM 2013

 The Abel Prize  Home page Springer Series  Proceedings Email nmf (at) math.ntnu.no

## Abstracts

You can find a pdf file with the program and abstracts here.

### Eric Bedford

#### Automorphisms of blowups of projective space

Abstract: We will discuss the existence of automorphisms and pseudo-automorphisms of complex manifolds which have positive entropy.

### Bo Berndtsson

#### The openness problem and complex Brunn-Minkowski inequalities

Abstract: The openness conjecture of Demailly-Kollár says that if $u$ is a plurisubharmonic function, then the set of all real numbers $t$ such that $e^{-tu}$ is locally integrable near a certain point, is open. I will give a proof of this and discuss the relation to complex Brunn-Minkowski inequlities.

### Zbigniew Błocki

#### Hörmander's $\bar\partial$-estimate, some generalizations and new applications

Abstract: We will present some new applications of the classical Hörmander's $L^2$ estimate for the $\bar\partial$ equation. Among them the Ohsawa-Takegoshi extension theorem with optimal constant, one-dimansional Suita conjecture, as well as Nazarov's approach to the Bourgain-Milman inequality in convex geometry.

### Jean-Pierre Demailly

#### On the cohomology of pseudoeffective line bundles

Abstract: The lecture will present various results concerning the cohomology of pseudoeffective line bundles on compact Kähler manifolds, twisted with corresponding multiplier ideal sheaves. In case the curvature is strictly positive in the sense of currents, the prototype is the well known Nadel vanishing theorem. We are interested here in the case where the curvature is merely semipositive. Various results and applications will be discussed, including a recent vanishing theorem due to Junyan Cao (forthcoming PhD thesis in Grenoble), and a study of simple compact Kähler 3-folds (joint work with F. Campana and M. Verbitsky from April 2013).

### Tien-Cuong Dinh

#### Positive closed (p,p)-currents and applications in complex dynamics

Abstract: I will present some recent progress in the study of positive closed currents of arbitrary bi-degree: regularization, super-potential, density and intersection. Several applications to dynamics will be given: entropy estimates, properties of dynamical degrees and equidistribution. The talk is based on joint works with Nessim Sibony.