EVENT DETAILS AND ABSTRACT

Title: Northwestern, Notre-Dame, UIC Complex Geometry Seminar: Geometric Partial Differential Equations from Unified String Theories
Speaker: D.H. Phong
Speaker Info: Columbia University
Brief Description:
Special Note:
Abstract:

he laws of nature at its most fundamental level have long been a source of inspiration for geometry and partial differential equations. With unified string theories and particularly supersymmetry, a particularly important new requirement has emerged, which is that of special holonomy. The earliest manifestation was identified by Candelas, Horowitz, Strominger, and Witten in 1985 as the Calabi-Yau condition, but more general spaces have emerged since, which can be interpreted as generalizations of Calabi-Yau spaces to both non-Kaehler complex geometry and symplectic geometry. The corresponding equations are interesting in their own right from the point of view of the theory of non-linear partial differential equations. We shall survey some of these developments, with emphasis on the analytic open problems.