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Symplectic Squeezing of Domains in T*Tn - Qi Feng

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Symplectic Squeezing of Domains in T*Tn Speaker: Qi Feng Affiliation: The Institute of Geometry and Physics (IGP) at University of Science and Technology of China Date: March 29, 2024 The symplectic squeezings in the cotangent bundle of a torus is distinct from those in R2n , due to the nontrivial topology of the torus. In this talk, we will show that for n≥2 any bounded domain of T∗Tn can be symplectically embedded into a trivial subbundle with an irrational cylinder fiber. These symplectic embeddings are constructed based on Arnold's cat map, Dirichlet's approximation theorem, and Bézout’s identity. Our result resolves an open problem posted by Gong-Xue (stated in n=2 ) and also generalizes it to higher dimensional situations. This talk is based on joint work with Jun Zhang