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Integrability in Pure Gravity and Classical Strings: Some Speculations

Integrability techniques offer ways of generating solutions to otherwise difficult problems. In the recent literature, such
techniques have been used to construct a host of (higher dimensional) gravitational backgrounds with diverse horizon topology. Similar
integrability techniques exist for the classical Polyakov string in certain backgrounds, including $AdS_5 \times S 5 $. One may hope to
gain control of these techniques, similar to the case for pure gravity, and construct classical string solutions of interest in
AdS/CFT. I will outline, in analogy to the gravitational case, how I hope to develop such control in the classical string case.