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Frobenius Manifolds And Virasoro Constraints
Boris Dubrovin, Youjin Zhang
For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation…
Geometry and analytic theory of Frobenius manifolds
Boris Dubrovin
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflec…
Monodromy of certain Painleve' VI transcendents and reflection groups
B. Dubrovin, M. Mazzocco
We study the global analytic properties of the solutions of a particular family of Painleve' VI equations with the parameters , and arbitrary. We introduce…
Painleve' transcendents and two-dimensional topological field theory
Boris Dubrovin
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 Fro…