Degenerate Double Affine Hecke Algebra and Conformal Field Theory.- Vertex Algebras.- Extensions of Conformal Modules.- String Duality and a New Description of the E6 Singularity.- A Mirror Theorem for Toric Complete Intersections.- Precious Siegel Modular Forms of Genus Two.- Non-Abelian Conifold Transitions and N = 4 Dualities in Three Dimensions.- GKZ Systems, Gröbner Fans, and Moduli Spaces of Calabi-Yau Hypersurfaces.- Semisimple Holonomic D-Modules.- K3 Surfaces, Igusa Cusp Forms, and String Theory.- Hodge Strings and Elements of K. Saito's Theory of Primitive Form.- Summary of the Theory of Primitive Forms.- Affine Hecke Algebras and Macdonald Polynomials.- Duality for Regular Systems of Weights: A Précis.- Flat Structure and the Prepotential for the Elliptic Root System of Type D4(1,1.- Generalized Dynkin Diagrams and Root Systems and Their Folding.
As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures.
The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
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