

International conference "Geometrical Methods in Mathematical Physics"
December 16, 2011 16:00–16:45, Moscow, Lomonosov Moscow State University






Gromov–Witten theory of orbifold projective lines and
integrable hierarchies
T. Milanov^{} ^{} Kavli Institute for the Physics and Mathematics of the Universe

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Abstract:
This is a joint work with H.H. Tseng and Y. Schen. Let $X$ be the sphere
with 3 orbifold points and a positive (orbifold) Euler characteristic. There
are finitely many such orbifolds and they are in 1to1 correspondence with
the Dynkin diagrams of type ADE. Our goal is to construct an integrable
hierarchy in the Hirota bilinear form that governs the Gromov–Witten
invariants of $X$. Following my earlier work with Givental and Frenkel, we
obtain a realization of the basic representation of the corresponding affine
Lie algebra in terms of the solutions of the quantum differential equations.
Once the representation is constructed we can identify our hierarchy with a
particular class of the so called Kac–Wakimoto hierarchies.
Language: English

