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

“辛场论的新挑战和新观点”国际会议将于2007年6月25日至29日在斯坦福大学举行。这将是第一次在这个主题上举行如此广泛的会议。会议将主办世界领先的数学家，包括著名的高级研究人员（唐纳森，Eliashberg，福谷，Gabai，Givental，Gromov，Hitchin，霍费尔，McDuff，维滕，..），但重点肯定是年轻的数学家和一些处于生产力顶峰的中期数学家。SFT处理代数不变量附加到辛流形接触边界。它捕获的几何形状的辛流形的内部（通过推广的Gromov-维滕不变量）和微妙的几何形状的Reeb轨道的接触边界组件。 它包括，在一个单一的框架，SFT的祖先，即辛和接触的同源性。会议将发生在一个关键时刻，当SFT和其他快速增长的数学深入研究的主题已经开始以最令人兴奋和有前途的方式相互作用。特别是，与新的低维拓扑不变量的关系，如Oszvath和Szabo，以及与新的Floer理论的发展（如分支Floer同调或集群复合物）和层次的可积系统将被探讨。外科手术，正则性和紧凑性问题将被讨论和各种应用结理论，动力系统，拉格朗日嵌入的拓扑结构也将是不同背景的专家之间的互动的焦点。“辛场论的新挑战和前景”国际会议（SFT）将于2007年6月25日至29日在斯坦福大学举行。这将是第一次在这个主题上举行如此广泛的会议。会议将举办世界领先的数学家，包括成熟的高级研究人员，但明确侧重于强大的年轻数学家和一些中期carreer数学家在其生产力的高峰。SFT处理整合的问题，在一个单一的强大的框架，几何的“内部拓扑”的周围空间的动力系统发生，与这些系统的封闭轨道的复杂行为。它的最终目的是了解在何种程度上的拓扑结构的周围空间决定定性行为的动力学规律。 它提出了许多深刻的，绝对迷人的分析和代数挑战，并与世界上许多迅速兴起的科学研究领域有关，如低维拓扑学（3维和4维）的最新发展或物理学家称为“可积系统和层次结构”的对象结构，这是过去50年来研究的一个复兴主题。

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.