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
