Symplectic Geometry originated mostly as the geometry of physical phase space underlying the dynamics of classical mechanics. Up to today, one of the most driving questions for those systems is that of stability and one of the most fundamental features of phase space dynamics is Poincare Recurrence which derives from the conservation of phase space volume. The seminal discovery due to Gromov and others that there is an intrinsic distinction between volume preservation and the invariance of the symplectic structure coined symplectic rigidity, however, left open the question, whether Poincare Recurrence also allows for a strictly stronger symplectic expression. In a way similar to the Arnold conjecture for Lagrangian intersections as an expression of symplectic rigidity, in this talk, I will propose a version of Symplectic Poincare Recurrence which will use a new kind of intersection result. The talk will address an audience of general geometric background.