24 jun 2025 -- 14:30
Aula Seminari, Dipartimento di Matematica, Pisa
Abstract.
In this talk, based on joint work with Stephane Geudens and Marco Zambon, we develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result is that each symplectic foliation is attached with a cubic $L_\infty$-algebra controlling its deformation problem. Indeed, we establish a one-to-one correspondence between the small deformations of a given symplectic foliation and the Maurer–Cartan 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 Maurer–Cartan elements. Finally, we show that the infinitesimal deformations of symplectic foliations can be obstructed.