By Dominic D. Joyce

This graduate point textual content covers an exhilarating and energetic quarter of analysis on the crossroads of numerous assorted fields in arithmetic and Physics. In arithmetic it comprises Differential Geometry, advanced Algebraic Geometry, Symplectic Geometry, and in Physics String idea and reflect Symmetry. Drawing widely at the author's prior paintings, the textual content explains the complicated arithmetic concerned easily and obviously to either mathematicians and physicists. beginning with the fundamental geometry of connections, curvature, advanced and Kähler constructions appropriate for starting graduate scholars, the textual content covers seminal effects resembling Yau's evidence of the Calabi Conjecture, and takes the reader all of the technique to the frontiers of present learn in calibrated geometry, giving many open problems.