Enumerative Invariants in Algebraic Geometry and String Theory: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 6–11, 2005

Dan Abramovich, Marcos Mariño, Michael Thaddeus, Ravi Vakil (auth.), Kai Behrend, Marco Manetti (eds.)3540798137, 9783540798132

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

Table of contents :
Front Matter….Pages I-X
Lectures on Gromov–Witten Invariants of Orbifolds….Pages 1-48
Lectures on the Topological Vertex….Pages 49-104
Floer Cohomology with Gerbes….Pages 105-141
The Moduli Space of Curves and Gromov–Witten Theory….Pages 143-198
Back Matter….Pages 199-210