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Tautological relations and the r -spin Witten conjecture

Carel Faber, Sergey Shadrin, Dimitri Zvonkine (2010)

Annales scientifiques de l'École Normale Supérieure

In [11], A. Givental introduced a group action on the space of Gromov–Witten potentials and proved its transitivity on the semi-simple potentials. In [24, 25], Y.-P. Lee showed, modulo certain results announced by C. Teleman, that this action respects the tautological relations in the cohomology ring of the moduli space ℳ ¯ g , n of stable pointed curves. Here we give a simpler proof of this result. In particular, it implies that in any semi-simple Gromov–Witten theory where arbitrary correlators can be...

The symbol of a function of a pseudo-differential operator

Alfonso Gracia-saz (2005)

Annales de l'institut Fourier

We give an explicit formula for the symbol of a function of an operator. Given a pseudo-differential operator A ^ on L 2 ( ℝ N ) with symbol A ∈ 𝒞 ∞ ( T * ℝ N ) and a smooth function f , we obtain the symbol of f ( A ^ ) in terms of A . As an application, Bohr-Sommerfeld quantization rules are explicitly calculated at order 4 in ℏ .

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