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In the talk we will rigorously define the full genus 0 stationary open
Gromov-Witten theory of maps to CP^1 with boundary conditions on RP^1,
including descendents, and shortly describe the equivariant version (which
is also constructed in genus 0).
We will then formally extend the localization construction to all genera,
and conjecture that this localization definition can really be made
geometrical. We shall show a strong evidence for the correctness of the
conjecture: Assuming it, an all genus open extension of the
Gromov-Witten/Hurwitz correspondence holds.
Joint work with A. Buryak, R. Pandharipande and A. Zernik.
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