Dipartimento di Matematica, Aula Magna.
In this talk we will report on ongoing work aiming to establish a Dubrovin conjecture for general Frobenius manifolds. The Dubrovin conjecture was formulated in 1998 (with a very precise statement in 2018) as a relation between the Frobenius manifold coming from the quantum cohomology of a Fano manifold $X$ and the derived category of coherent sheaves of $X$. We will give some speculations about how to extend that relation to one between semisimple Frobenius manifolds and some categories. We will sketch the situation in a particular example (3-point Ising model).
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