Title: Noncommutative resolutions and Coulomb branches

Abstract: One of the fascinating interfaces between mathematics and quantum field theory in recent years has been through 3d N=4 theories and their topological twists.  The portions of a topologically twisted theory most readily understood by mathematicians are the point (i.e. local) and line operators.  The former are mathematically captured by a symplectic singularity, and the latter give insight into the category of coherent sheaves on resolutions of this singularity.

In particular, if we consider the A-twist of linear gauge theories, we obtain the Coulomb branch as defined by Braverman-Finkelberg-Nakajima, and the vortex line operators of this theory give us insight in the category of coherent sheaves on (both usual and noncommutative) symplectic resolutions of this variety.  I’ll discuss this construction and how it gives a mathematical approach to Aganagic’s “type B” knot homology, and shows that it matches previous constructions of knot homology.