On classification and construction of algebraic Frobenius manifolds

Yassir Dinar (Scuola Internazionale Superiore di Studi Avanzati)

Tuesday 16th November, 2010 15:00-16:00 Mathematics Building, room 515


I will speak about a work in progress to prove Dubrovin conjecture on classification of algebraic Frobenius manifolds. The conjecture is stated as follows: semisimple algebraic Frobenius manifolds correspond to quasi-Coxeter conjugacy classes in Coxeter groups. I will give some details about the construction of nontrivial algebraic Frobenius manifolds which support this conjecture. These manifolds are obtained from the classical $W$-algebras associated to the subregular nilpotent orbits in the Lie algebra of type $D_r$, $r$ is even or $E_r$, $r=6,7,8$. These manifolds are certain hypersurfaces in the total spaces of semiunivesal deformation of the simple singularities of the same type.

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