In this talk, based on joint work with Stephane Geudens and Marco Zambon, I develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leaf-wise symplectic form. The main result is that each symplectic foliation is attached with an L_\infty algebra controlling its deformation problem. Indeed, we establish a one-to-one correspondence between the small deformations of a given symplectic foliation and the MC elements of the associated L_\infty algebra. Further, we prove that, under this one-to-one correspondence, the equivalence by isotopies of symplectic foliations agrees with the gauge equivalence of MC elements. Finally, we show that the infinitesimal deformations of symplectic foliations can be obstructed.
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