239 citations · 567 across the 22 of their papers we have counts for
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Semi-infinite variations of Hodge structures and integrable hierarchies of KdV type
Serguei Barannikov
We introduce integrable KdV type hierarchy associated naturally with arbitrary semi-simple Frobenius manifold. We present hierarchy in a Lax form and show that it admits bihamilton…
Semi-infinite Hodge structures and mirror symmetry for projective spaces
S. Barannikov
We express total set of rational Gromov-Witten invariants of projective spaces via periods of variations of semi-infinite Hodge structure associated with their mirror partners.
Quantum periods - I. Semi-infinite variations of Hodge structures
S. Barannikov
We introduce a generalization of variations of Hodge structures living over moduli spaces of non-commutative deformations of complex manifolds. Hodge structure associated with a po…
Generalized periods and mirror symmetry in dimensions n>3
Sergey Barannikov
The predictions of the Mirror Symmetry are extended in dimensions n>3 and are proven for projective complete intersections Calabi-Yau varieties. Precisely, we prove that the total…