Rigidity asserts that certain special characteristics of a system are enough to identify it among a large class of systems. One of the most famous conjectures in dynamical rigidity is the Birkhoff conjecture, which claims that the only integrable billiards are ellipses. After the breakthrough work of Avila, De Simoi, Kaloshin, Sorrentino, Bialy, Mironov, etc, steady progress continued to emerge, including results by proposed speakers Koval, Koudjinan, Sorrentino, Massetti, and Tsodikovitch. A closely related question, "Can you hear the shape of a drum?" asks whether Laplace spectral information determines the shape of the billiard. Many of the proposed speakers (and some organizers) have been main contributors to the most recent development in this area – we mention the work of De Simoi, Kaloshin, Leguil, and Osterman on hyperbolic billiards, Sorrentino, Vig, and Nardi on symplectic billiards, Li on analogous problems in the Standard map. For analytic billiards, Baldomà, Florio, Leguil, and Seara studied the generic properties of Birkhoff periodic orbits. 

 

A flip side of integrability and rigidity is the question of diffusion, which asserts that a typical perturbation can destroy integrability. This has been one of the central questions in Hamiltonian systems since Poincaré. A particularly important application is to celestial mechanics. Many proposed speakers and organizers have been contributors to this area – we mention the work of Kaloshin and Zhang on generic diffusion in smooth systems, Fayad, Trujillo, Seara, Paradela on analytic systems, and Guardia, Seara, Paradela, and Fejoz, who are involved in a series of impressive applications to celestial mechanics. 

 

We will invite speakers that represent a wide range of areas within Hamiltonian systems and dynamics overall. In addition to the aforementioned areas, we will invite experts in KAM theory,  in exponentially small splitting, in universal dynamics, in resonances, and in weak KAM theory and symplectic dynamics.

 

We aim to facilitate collaborative exchange between researchers working in these fields and related disciplines, cultivating interdisciplinary dialogue. We are committed to nurturing the next generation of researchers by actively encouraging the participation of graduate students, postdoctoral fellows and emerging scholars.