Symplectic Squeezing of Domains in T*Tn

The symplectic squeezings in the cotangent bundle of a torus is distinct from those in $R^{2n}$, due to the nontrivial topology of the torus. In this talk, we will show that for $n\ge2$ any bounded domain of $T^*T^n$ 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