Special Year on Conformally Symplectic Dynamics and Geometry

During the 2026-27 academic year the School will have a special program on Conformally Symplectic Dynamics and Geometry. Michael Hutchings, University of California, Berkeley will be the Distinguished Visiting Professor.

The purpose of this special year is to investigate the relations of conformally symplectic dynamics with classical symplectic dynamics, to understand the new phenomena that appear, and to develop associated geometric structures, such as locally conformal symplectic manifolds. Symplectic dynamics studies the dynamics of symplectic maps, Hamiltonian vector fields, and Reeb vector fields on contact manifolds. There have been some recent breakthroughs in symplectic dynamics using Floer theoretic techniques, for example the proofs of smooth closing lemmas in low dimensions. Conformal symplectic dynamics is an extension of symplectic dynamics in which the symplectic form is rescaled and not necessarily preserved, which allows for dissipative behavior. Some well established results of symplectic dynamics have natural extensions to the conformal setting (for example KAM theory, Aubry-Mather subsets, Arnold diffusion, and rigidity results for invariant manifolds), while there are new phenomena special to the dissipative case, such as Birkhoff attractors. 

The goal of the program is to bring together experts in symplectic geometry, dynamics, PDE, and applications, in order to exchange ideas between subfields and develop the broader world of conformally symplectic dynamics and geometry.

Senior participants: Marie-Claude Arnaud, Tere Seara, Alfonso Sorrentino, Claude Viterbo.