Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4

general topology

Banff International Research Station

Audience:	Researchers in the topic
Seminar series times:	No fixed schedule
Organizer:	BIRS Programme Coordinator*
	*contact for this listing

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This workshop will highlight new results in low-dimensional topology coming from a wide range of geometric methods. Low-dimensional topology studies the global properties of geometric spaces in dimensions 3 and 4, such as 3-dimensional space and 4-dimensional space-time. Surprisingly, the study of spaces in dimensions 3 and 4 is more challenging than in higher dimensions: for instance, the famous Poincaré conjecture, which gives an intrinsic topological characterization of the sphere, was solved recently by Perelman in dimension 3, and has not yet been completely settled in dimension 4, while its higher dimensional generalizations were previously known. In fact, studying 3- and 4-dimensional spaces requires combining a variety of different approaches, many of which are geometric in nature and have their roots in theoretical physics. Much of the recent progress in this extremely active area of mathematics makes use of the interplay between sophisticated mathematical invariants (quantities that can be used to distinguish one space from another) coming from gauge theory and from contact and symplectic geometry, and clever new cut-and-paste constructions that modify known spaces in surprising ways. The workshop will feature new discoveries on the shape of space and knotted objects inside space, and will host leading experts from around the world.

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