00912nas a2200145 4500008004100000245010700041210006900148260001000217520041300227100002000640700002400660700001800684700001600702856004800718 2015 en d00aExtended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials0 aExtended affine Weyl groups of BCD type Frobenius manifolds and bSISSA3 aFor the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures.1 aDubrovin, Boris1 aStrachan, Ian, A.B.1 aZhang, Youjin1 aZuo, Dafeng uhttp://preprints.sissa.it/handle/1963/3531600982nas a2200133 4500008004100000245007000041210006300111260001000174520057500184100002000759700001500779700001800794856003600812 2012 en d00aOn the genus two free energies for semisimple Frobenius manifolds0 agenus two free energies for semisimple Frobenius manifolds bSISSA3 aWe represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.1 aDubrovin, Boris1 aLiu, Si-Qi1 aZhang, Youjin uhttp://hdl.handle.net/1963/646400348nas a2200109 4500008004100000245005600041210005600097260001100153100002000164700001800184856003600202 1998 en d00aExtended affine Weyl groups and Frobenius manifolds0 aExtended affine Weyl groups and Frobenius manifolds bKluwer1 aDubrovin, Boris1 aZhang, Youjin uhttp://hdl.handle.net/1963/6486