Yakov Eliashberg: Rigidity and Flexibility in Symplectic Geometry

Symplectic topology was born in the 1980s on the borderline between the worlds of rigid and flexible mathematics. In the talk I will describe some recent advances on both sides of the border. On the
flexible side, I will discuss a surprising h-principle for Legendrian knots of dimension>1, proven by my student Max Murphy, as well as its consequences for symplectic topology of Stein manifolds. On the rigid
side, I will discuss effective techniques for computing symplectic invariants of Stein manifolds via Legendrian surgery. The flexible side of the story is joint work with K. Cieliebak, and the rigid one with F. Bourgeois and T. Ekholm.