@article {2015, title = {Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials}, year = {2015}, institution = {SISSA}, abstract = {For 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.}, url = {http://preprints.sissa.it/handle/1963/35316}, author = {Boris Dubrovin and Ian A.B. Strachan and Youjin Zhang and Dafeng Zuo} } @article {2012, title = {On the genus two free energies for semisimple Frobenius manifolds}, journal = {Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298}, number = {arXiv:1205.5990;}, year = {2012}, note = {36 pages, 3 figures}, publisher = {SISSA}, abstract = {We 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.}, doi = {10.1134/S1061920812030028}, url = {http://hdl.handle.net/1963/6464}, author = {Boris Dubrovin and Si-Qi Liu and Youjin Zhang} } @article {1998, title = {Extended affine Weyl groups and Frobenius manifolds}, journal = {Compositio Mathematica. Volume 111, Issue 2, 1998, Pages 167-219}, year = {1998}, publisher = {Kluwer}, doi = {10.1023/A:1000258122329}, url = {http://hdl.handle.net/1963/6486}, author = {Boris Dubrovin and Youjin Zhang} }