Workshop on Topology and Invariants of 4-Manifolds: August 23 – 27, 2014

Application for workshop is now closed.

Organized by Selman Akbulut (Michigan State), Anar Akhmedov (University of Minnesota, Twin Cities), Mehmet Firat Arikan (METU), Weimin Chen (University of Massachusetts, Amherst), Yasha Eliashberg (Stanford University), Cagri Karakurt (University of Texas, Austin), Tian-Jun Li (University of Minnesota, Twin Cities), Danny Ruberman (Brandeis University), and Nikolai Saveliev (University of Miami)

Dates: August 23 – 27, 2014

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With the advent of gauge theories and the developments of symplectic topology and the 4-dimensional handlebody techniques, the field of 4-manifolds has experienced a period of phenomenal growth and development. By using gauge theory, Donaldson showed that smooth 4-manifolds are very different from their higher dimensional counterparts. For example, four is the only dimension in which a fixed homeomorphism type of closed 4-manifolds can be represented by infinitely many diffeomorphism types, and in which there exist exotic R^4, that is, manifolds homeomorphic but not diffeomorphic to R^4. Further results followed with the development of Seiberg-Witten gauge theory, which significantly simplified and extended use of gauge theory in the topology of 4-manifolds. Taubes related the Seiberg-Witten and Gromov-Witten invariants of symplectic 4-manifolds, thereby establishing a very important link between smooth and symplectic topology. Ever since, techniques from symplectic and contact topology have provided some of the most important tools in low-dimensional topology, making available a number of new invariants for the study of a large class of smooth 4-manifolds.

Our workshop will bring together leading researchers working in the fields of three- and four-dimensional topology, gauge theory, contact and symplectic topology as well as some researchers in the topology of higher dimensional geometric structures. The workshop will provide an opportunity to initiate and enhance the interaction, exchange of ideas, and possible collaboration between the participants. We expect that the workshop will also present an opportunity for the participants to learn the recent advances as well as to reflect upon on previous known techniques for studying the smooth and symplectic 4-manifolds, and contact 3-manifolds. Specifically, we plan to focus on the following research topics: Invariants of Smooth 4-Manifolds, Symplectic Topology, Exotic Group Actions on 4-Manifolds, Exotic 4-Manifolds, Handlebodies of Exotic 4-Manifolds, Stein Fillings and Contact 3-Manifolds, and the Topology of higher dimensional geometric structures.

All workshop talks will be held in the Simons Center Lecture Hall (Room 102).

***Please note: Both Saturday 8/23 and Sunday 8/24 will be informal days of the workshop. We will not have our full staff around on these two days (talks will still be recorded and there will be one other staff member present).

2013 FRG Workshop and Conference: Topology and Invariants of Smooth 4-Manifolds
http://www.math.umn.edu/~akhmedov/UMN2013

2012 FRG Workshop and Conference: Topology and Invariants of Smooth 4-Manifolds
http://www.math.umn.edu/~akhmedov/Stanford2012