Vortices, Monopoles, and Finite AGT

In three-dimensional gauge theories, monopole generators create and annihilate vortex particles. I will explore this basic idea in the context of 3d N=4 theories placed in an Omega background. In some cases, what results is a "finite" version of the AGT correspondence (first proposed by Braverman-Feigin-Finkelberg-Rybnikov), involving an action of finite W-algebras on the equivariant cohomology of vertex moduli spaces. In general, we find a far-reaching extension of this construction. (Work with M. Bullimore, D. Gaiotto, J. Hilburn, H.C. Kim.)

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