Painleve' transcendents and two-dimensional topological field theory

Abstract

Lecture 1. Algebraic properties of correlators in 2D topological field theory. Moduli of a 2D TFT and WDVV equations of associativity. Lecture 2. Equations of associativity and Frobenius manifolds. Deformed flat connection and its monodromy at the origin. Lecture 3. Semisimplicity and canonical coordinates. Lecture 4. Classification of semisimple Frobenius manifolds. Lecture 5. Monodromy group and mirror construction for semisimple Frobenius manifolds.

117 pages, plain TeX, no figures References added; to appear in Proceedings of 1996 Cargèse school ``The Painlevé property: one century later''

References in corpus (11)

• Geometry and Integrability of Topological-Antitopological Fusion
• Equivariant Gromov - Witten Invariants
• Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of ${\mathbf{P}}^2$
• Quantum Cohomology of a Product
• Elliptic Gromov - Witten invariants and the generalized mirror conjecture
• A mirror theorem for toric complete intersections
• Constraints For Topological Strings In $D\ge 1$
• Quantum and Floer cohomology have the same ring structure
• Quantum intersection rings
• Primitive Forms, Topological LG models coupled to Gravity and Mirror Symmetry
• Frobenius Manifolds from Yang-Mills Instantons

Cited by in corpus (7)

• Stability conditions and the $A_2$ quiver
• Crepant resolutions and open strings
• Formulas for A_n and B_n-solutions of WDVV equations
• Profiling the Brane Drain in a Nonsupersymmetric Orbifold
• Mirror symmetry for extended affine Weyl groups
• The Period map for quantum cohomology of ${\mathbb{P}}^2$
• Hirota Quadratic Equations for the Gromov--Witten Invariants of ${\mathbb{P}}_{n-2,2,2}^1$