Colóquio 

19/07/2001, 17:00 — 18:00 — Anfiteatro Ga1, Pavilhão Central, IST
François Lalonde, Université de Montréal

Geometry and dynamics: towards a $L^{\infty }$-theory

Techniques of elliptic PDE's in the context of gauge theory as well as in symplectic topology have led to solutions of deep problems on the existence and behavior of periodic orbits of arbitrary Hamiltonian systems. They have also led to a much better knowledge of smooth and symplectic structures on manifolds, especially in dimension 4. Using Quantum homology and its relation with Floer homology, I will describe how this is now paving the way to the emergence of a new $L^{\infty }$-theory that has both geometric and dynamic interpretations.