Department of

September 2017 October 2017 November 2017 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 1 2 3 4 5 6 7 1 2 3 4 3 4 5 6 7 8 9 8 9 10 11 12 13 14 5 6 7 8 9 10 11 10 11 12 13 14 15 16 15 16 17 18 19 20 21 12 13 14 15 16 17 18 17 18 19 20 21 22 23 22 23 24 25 26 27 28 19 20 21 22 23 24 25 24 25 26 27 28 29 30 29 30 31 26 27 28 29 30

Monday, October 30, 2017

**Abstract:** Gromov's Non-Squeezing Theorem is a remarkable result in symplectic geometry. It says that the ball $B^{2n}(r)$ of radius $r$ in ${\mathbb R}^{2n}$ can be symplectically embedded in the "cylinder" $B^2(R)\times {\mathbb R}^{2n-2}$ of radius $R$ only if $r\le R$. The proof uses so called J-complex (pseudoholomorphic) curves. We will describe a construction of J-complex disks based on the classical scheme for solving the Beltrami equation in complex analysis. We will discuss related results and open problems.