IHP: Program in Conformal and Kahler Geometry

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

This grant will support a program in the Fall of 2012 at the Institut Henri Poincare in Paris, France, on the theme of Conformal and Kahler geometry. The trimester will begin with two introductory mini-courses followed by the week-long conference Conformal and Kahler Geometry (September 17-21), which will cover the broad mathematical themes of the program: conformal invariants, Poincaré-Einstein metrics, self-duality, nonlinear PDEs in conformal geometry, critical Kahler metrics, and complex Monge-Ampere equations. The other activities throughout the trimester will attempt to elaborate and bring into sharper focus the developments related in the introductory conference. There will be three smaller and more focused workshops later in the term: Geometry and Physics (October 8-12), Geometric PDE (November 5-9), and Recent Developments in Kahler Geometry (December 10-14). These will be accompanied by a series of topical mini-courses. Conformal geometry has its origins in the study of functions of a complex variable in the nineteenth century. Roughly speaking, it is the study of transformations of a space which may distort the measurement of distances, but not how one measures angles. Conformal mappings play a basic role in many applied sciences, and modern conformal geometry has connections to theoretical physics and materials science. Kahler geometry is a branch of complex geometry which also has important ties to physics and many areas of modern geometry. The goals of this program are to provide an overview of the current state of the field in these areas, foster interactions between researchers and educate graduate students and postdoctoral scholars on open problems and recent techniques.