The Infinite Dimensional Frobenius Manifold of 2D Toda Hierarchy

The first chapter is a brief review on Frobenius manifolds and integrable systems. In the second chapter we recall the construction of the bihamiltonian structure for the 2D Toda hierarchy using R-matrix theory. Although the procedure is the same as in [11], a new R-matrix is proposed to provide a new bihamiltonian structure in the dispersionless limit. In the third chapter the Frobenius manifold M2DT is defined. We provide explicit formulae for the 3-point correlator function and the intersection form. Moreover, we prove that M2DT is semi simple by defining the canonical coordinates. The last chapter is devoted to the principal hierarchy.