Recent advances in complex differential geometry  Program
Summer School: June 1317, 2016
Minicourses by

Bo Berndtsson: "Complex BrunnMinkowski Theory and Applications"
In the first lecture we will present some background in convex geometry, the BrunnMinkowski inequality, the Alexander Fenchel inequality and the PrekopaLeindler inequality. In the second lecture we will discuss some theorems on positivity of holomorphic vector bundles and argue that they can be seen as complex analogs of (some of) the results on convexity from the first lecture. We will also sketch some applications of these results, related to the convexity of Kenergy and the OhsawaTakegoshi theorem. After that we will discuss a more recent generalization of these methods to the study of variations of complex structures; this last part is (ongoing, i e. not completely finished) joint work with Xu Wang.
In this series of lectures, we will survey a number of recent results related to positivity : positive cones, intersection theory of chomology classes, duality results, multiplier ideal sheaves, vanishing and extension theorems. We will also try to discuss several a few open problems connected to these questions (existence of rational curves, abundance conjecture, transcendental Morse inequalities, deformations of Kähler manifolds ...)

Duong H. Phong: “Nonlinear Partial Differential Equations in Complex Geometry"
This series of lectures will be devoted to an informal and mostly selfcontained survey of some nonlinear partial differential equations arising in complex geometry. Starting from the classical theory of the YangMills equation on holomorphic vector bundles, we shall discuss topics ranging from the Ricci flow on Riemann surfaces with conic singularities, to elements of the theory of fully nonlinear equations, and to recent equations from nonK\”ahler geometry such as the Gauduchon conjecture, the FuYau equations, and Strominger systems.
Conference: June 17June 22, 2016
Minicourses by

David Calderbank: "Projective Equivalence in Kähler Geometry"

Philippe Eyssidieux: "KählerEinstein Fano Varieties"

Andrei Teleman: "On the Classification of NonKähler Surfaces"
Speakers :
 V. Apostolov (UQAM)
 T. Collins (Harvard Univ.)
 V. Datar (UC Berkeley)
 R. Dervan (Univ. of Cambridge)
 T. Delcroix (Univ. de Grenoble)
 A. Fino (Univ. of Torino) Slides of A. Fino's talk: AFinoToulouse2016main.pdf
 L. Foscolo (Stony Brook Univ.)
 C. Lu (Scuola Normale, Pisa)
 G. Marinescu (Univ. of Cologne)
 T. Murphy (Cal State Fullerton) Slides of T. Murphy's talk: TMurphyToulousetalk.pdf
 D. Panov (King's College, London)
 C. Spotti (Univ. of Cambridge)
 D. W. Nyström (Univ. of Gothenburg)
 B. Taji (Univ. of Freiburg)
 X. Wang (Rutgers Univ.)
 J. Xiao (Univ. de Grenoble)
Abstracts and titles of the 1h talks can be found here : titlesabstracts.pdf