Northeast Conferences on Geometry and Topology of 4-Manifolds

“东北四维流形的几何和拓扑学会议”系列将在2015-2016年间举行两次会议，均在马萨诸塞大学阿默斯特分校举行。第一次会议将于2015年4月24-26日举行，主题为“辛四维流形的几何与拓扑”，第二次会议将于2016年秋季举行，主题为“四维流形的Floer同调、规范理论与拓扑”。会议系列聚焦于四维流形的几何和拓扑，被视为各种研究领域的熔炉，如低维拓扑学、接触、辛、复几何和微分几何、几何分析和数学物理。组织者计划将来自全国各地的顶尖专家和崭露头角的年轻研究人员聚集在一起，作为每次会议的演讲者，并支持感兴趣的研究人员和研究生参与，特别是来自东北地区机构的参与。会议系列的一个目标是通过加强马萨诸塞州、纽约、新泽西州和康涅狄格州的地质学家和拓扑学家之间的互动和合作，特别是研究生、初级研究人员和他们的资深同事之间的互动和合作，促进新的研究方向，同时通过各种讲座和讨论为所有人提供该主题领域的全景。该系列将有助于建立一个区域网络，并支持整个东北地区的研究生、教师和其他研究人员之间的联系。这两个会议的主题都是从近年来最活跃和最具活力的领域中挑选出来的。Taube将Seiberg-Witten规范理论和辛拓扑联系起来的工作对辛几何和四维光滑拓扑都产生了巨大的影响，而Donaldson和Gompf的工作则导致了Lefschetz原函数的许多新的构造和应用。这些进展使人们对辛四维流形的内部结构有了更深入的了解。值得注意的是，这导致了负Kodaira维辛四维流形的完全光滑辛分类。这些将是第一次会议的主要议题。另一方面，规范理论对光滑四维流形的研究产生了巨大的影响，始于唐纳森在20世纪80年代的开创性工作，S，以及大约10年后Seiberg-Witten理论的引入。再加上构造4-流形的新方法，这导致了许多同伦类型的奇异光滑流形的构造，并使人们对光滑4-流形的内部结构有了更深的理解。最近几年最深入的结果是基于三维流形的规范理论不变量的使用，这些不变量被称为Floer同调理论，这反过来又得到了带边界的四维流形的不变量。第二次会议将集中讨论所有光滑4-流形的这些不变量。2015年春季会议的网络链接：http://people.math.umass.edu/~baykur/Symplectic4manifoldsConference.html

The "Northeast Conferences on Geometry and Topology of 4-manifolds" series will have two meetings in 2015-2016, both at the University of Massachusetts, Amherst. The first conference, entitled "Geometry and Topology of Symplectic 4-Manifolds," will meet between April 24-26, 2015, and the second, entitled "Floer Homologies, Gauge Theory, and Topology of 4-Manifolds," will meet in fall 2016. The conference series focuses on the geometry and topology of 4-manifolds, regarded as a melting pot for various research areas, such as low dimensional topology, contact, symplectic, complex and differential geometry, geometric analysis, and mathematical physics. The organizers plan to bring together leading experts and rising young researchers from across the country as speakers for each meeting and to support participation of interested researchers and graduate students, especially from the institutions in the Northeast. An objective of the conference series is to fertilize new research directions by increasing interaction and collaboration among the wealth of geometers and topologists in Massachusetts, New York, New Jersey and Connecticut, particularly among graduate students, junior researchers, and their more senior colleagues, while providing all with a panorama of the subject area through a variety of talks and discussion sessions. The series will help build a regional network and support ties among graduate students, faculty, and other researchers throughout the Northeast.The themes for both conferences are chosen from the most active and dynamic fields in recent years. Taubes' work connecting Seiberg-Witten gauge theory and symplectic topology has had great impact on both symplectic geometry and 4-dimensional smooth topology, while work of Donaldson and Gompf has led to many new constructions and applications of Lefschetz fibrations. The advances led to deep understanding of the internal structure of symplectic 4-manifolds. Remarkably, this led to the complete smooth and symplectic classification of symplectic 4-manifolds of negative Kodaira dimension. These will be the main topics of the first conference. On the other hand, gauge theory has had an enormous impact on the study of smooth 4-manifolds, starting with the seminal work of Donaldson in the 1980's and the introduction of Seiberg-Witten theory some 10 years later. Coupled with new methods for building 4-manifolds, this has led to the constructions of exotic smooth manifolds in many homotopy types, and to an understanding of the internal structure of smooth 4-manifolds. The deepest results of recent years have been based on the use of gauge theoretic invariants of 3-manifolds known as Floer homology theories, which give rise in turn to invariants of 4-manifolds with boundary. The second conference will focus on these invariants for all smooth 4-manifolds.Web link for the Spring 2015 conference: http://people.math.umass.edu/~baykur/Symplectic4manifoldsConference.html