Low Dimensional Topology and Gauge Theory (17w5040)

Arriving in Oaxaca, Mexico Sunday, August 6 and departing Friday August 11, 2017

Organizers

(Brandeis University)

Anar Akhmedov (University of Minnesota)

(Princeton University)

Yi-Jen Lee (Chinese University of Hong Kong)

David Auckly (Kansas State University)

Objectives

There are many fundamental open problems in the theory of smooth 4-manifolds. At the same time there has been steady progress in the field. The most effective tool has been gauge theory. The first gauge theoretic information about 4-manifolds came from the Yang-Mills equations. Later, the Seiberg-Witten equations transformed the field, to be followed by the development of Heegaard Floer theory. It is a reasonable conjecture that the invariants arising from all three packages agree, and there are a number of partial results to support this. It is more difficult to compare the associated invariants of 3-manifolds or knots. There are many interesting variants and gauge-theoretic tools in 3-dimensions, and the interplay between these various tools is an interesting area of current research.

At the same time progress continues on various construction techniques. New examples continue to be discovered and existing examples are becoming better understood. This conference will bring together researchers who study smooth topology in dimension four with researchers who study the various forms of gauge theory.