Perspectives in topology and geometry of 4-manifolds

University Of Georgia Research Foundation Inc, Athens GA

Investigators

Abstract

The international conference on Perspectives in Topology and Geometry of 4-manifolds will be held June 5--10, 2016 at the Inter University Centre in Dubrovnik, Croatia. This conference will bring together leading researchers and emerging mathematicians in 4-dimensional topology and geometry from around the world, with the aims of providing directions for future research on open problems in the subject and introducing younger mathematicians to the field. NSF funds will be used to defray travel and lodging expenses for participants based in the US, with priority for invited speakers, and for junior mathematicians without other sources of funding. The conference will have an impact in fostering communication and collaboration between topologists at various career stages, providing perspective and new research directions for young mathematicians. Modern 4-manifold theory can be said to have begun in the early 1980s with the work of Donaldson applying gauge theory. Since 2000, the attention of many low-dimensional topologists has shifted to dimension 3, where Floer-theoretic invariants have allowed remarkable progress. However, some of the most striking applications of these invariants of 3-manifolds, and from a certain point of view the philosophical motivation for the invariants themselves, relate to 4-manifolds either directly or through the techniques involved. Moreover, there are a number of fundamental unsolved problems in 4-manifold theory that may yield to new ideas rooted in Floer theory. The conference will serve the dual function of publicizing the newest ideas and approaches to these unsolved problems, and of introducing a younger generation to 4-manifold theory. With participation by some of the preeminent leaders in the field as well as many talented younger mathematicians, the organizers hope that this conference will touch off new activity and progress in 4-manifold topology. As a part of the conference we also plan to celebrate the work of Ron Fintushel and Ron Stern which has been very influential in the development of the field. The organizers will edit and publish a volume of proceedings associated with this conference, with contributions from many of the speakers. The centerpiece of the volume will be a section devoted to open problems in 4-manifold topology based on problem sessions run during the conference by Rob Kirby, Ron Fintushel and Ron Stern. Further details can be found on the conference webpage, https://www.renyi.hu/~ldtbud/Dubrovnik/