Sino-Russian Mathematics Center-JLU Colloquium (2024-031)—Deformations of Symplectic Foliations

Title: Deformations of Symplectic Foliations
Speaker: Alfonso Giuseppe TORTorella
Institution: University of Salerno
Date & Time: November 7, 2024, 20:00–21:00
Location: Zoom ID: 904 645 6677, Password: 2024

In this talk, based on joint work with Stéphane 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 associated with a cubic $L_{\infty }$-algebra that governs its deformation problem. Specifically, 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. Furthermore, we prove that under this correspondence, the isotopy equivalence of symplectic foliations aligns with the gauge equivalence of Maurer–Cartan elements. Finally, we demonstrate that the infinitesimal deformations of symplectic foliations can be obstructed.

Alfonso Giuseppe TORTorella earned his PhD from the University of Florence in 2017 and is currently an Assistant Professor of Geometry at the University of Salerno. His research focuses on the geometry of Poisson and related structures, with a primary emphasis on deformation problems in Poisson geometry.