An International Conference on: New Challenges and Perspectives in Symplectic Field Theory

Stanford University, Stanford CA

Investigators

Abstract

The international Conference on ``New Challenges and Perspectives in Symplectic Field Theory (SFT)'' will take place at Stanford University, June 25--29, 2007. This will be the very first conference of such amplitute to be held in this subject. The Conference will host the world's leading mathematicians including the well established senior researchers (Donaldson, Eliashberg, Fukaya, Gabai, Givental, Gromov, Hitchin, Hofer, McDuff, Witten, ...), but with a definite focus on strong younger mathematicians and some mid-carreer mathematicians at the peak of their productivity. SFT deals with algebraic invariants attached to symplectic manifolds with contact boundaries. It captures both the geometry of the interior of the symplectic manifold (through a generalization of the Gromov- Witten invariants) and the subtle geometry of the Reeb orbits of the contact boundaries components. It includes, in a single framework, the ancestors of SFT, i.e the symplectic and contact homologies. The Conference will happen at a crucial moment when SFT and other rapidly growing subjects of intensive research in mathematics have begun to interact in the most exciting and promising way. In particular, the relations with new low dimensional topological invariants, eg those of Oszvath and Szabo, as well as with new Floer theoretical developments (eg the Branching Floer Homology or the Cluster complexes) and with hierarchies of integrable systems will be explored. Surgery, regularity and compactness problems will be discussed and various applications to knot theory, dynamical systems, the topology of Lagrangian embeddings will also be the focus of interactions amongst specialists of diverse backgrounds. The international conference on ``New Challenges and Perspectives in Symplectic Field Theory (SFT)'' will take place at Stanford University, June 25--29, 2007. This will be the very first conference of such amplitute to be held in this subject. The Conference will host the world's leading mathematicians including the well established senior researchers but with a definite focus on strong younger mathematicians and some mid-carreer mathematicians at the peak of their productivity. SFT deals with the problem of integrating, in a single powerful framework, the geometry of the ``internal topology'' of ambient spaces where dynamical systems occur, with the intricate behaviour of closed orbits of these systems. Its ultimate aim is to understand to which extent the topology of ambient spaces determines the qualitative behaviour of dynamical laws. It poses lots of deep, absolutely fascinating analytical and algebraic challenges and bears relations to many rapidly emerging fields of scientific investigation in the world, like the recent development in low dimensional topology (in dimension 3 and 4) or the structure of objects known to physicists as ``integrable systems and hierarchies'' that have been a resurgent theme of research over the last fifty years.