From symplectic embeddings to number theory II
Responsable du projet | Félix Schlenk |
Collaborateur | Clémence Labrousse |
Résumé |
Symplectic geometry is the geometry underlying Hamiltonian dynamics,
and symplectic mappings arise as time 1 maps of Hamiltonian flows.
In the last three decades, spectacular rigidity phenomena for
symplectic mappings were discovered that show that symplectic
mappings are much more special than volume preserving mappings.
Recently, McDuff and Schlenk computed the function giving for each
r the radius of the smallest 4-dimensional ball into which the
4-dimensional ellipsoid E(1,r) symplectically embeds, and Frenkel
and Müller computed the function giving for each r the radius
of the smallest 4-dimensional cube into which E(1,r) symplectically
embeds. These works show that sometimes, the structure of symplectic
rigidity is rich: The graph of both functions is surprisingly
complicated. It is given in part in terms of Fibonacci and Pell
numbers. Along the proof, Diophantine systems, very special
solutions to these systems, and many other number theoretic
quantities, relations and identities appear in a rather mysterious
way. Around the same time, Hutchings and McDuff have answered the
Hofer conjecture, by giving a combinatorial recipe telling whether
one 4-dimensional ellipsoid symplectically embeds into another such
ellipsoid. The goal of this project is to determine the
corresponding embedding functions. In this way, we hope to better
understand the structure of symplectic rigidity in an interesting
class of examples. |
Mots-clés |
Symplectic geometry |
Type de projet | Recherche fondamentale |
Domaine de recherche | Mathématiques |
Source de financement | FNS - Encouragement de projets (Div. I-III) |
Etat | Terminé |
Début de projet | 1-10-2012 |
Fin du projet | 30-9-2015 |
Budget alloué | 302'838.00 |
Autre information |
http://p3.snf.ch/projects-144432# |
Contact | Félix Schlenk |