  Given a representation N of a reductive group G,
Braverman-Finkelberg-Nakajima have defined a remarkable Poisson variety called
the Coulomb branch. Their construction of this space was motivated by
considerations from 3d gauge theories and symplectic duality. The coordinate
ring of this Coulomb branch is defined as a convolution algebra, using a vector
bundle over the affine Grassmannian of G.
  This vector bundle over the affine Grassmannian maps to the space of loops in
the representation N. We study the fibres of this maps, which live in the
affine Grassmannian. We use these BFN Springer fibres to construct modules for
(quantized) Coulomb branch algebras. These modules naturally correspond to
boundary conditions for the corresponding gauge theory.
  We use our construction to partially prove a conjecture of
Baumann-Kamnitzer-Knutson and give evidence for conjectures of Hikita,
Nakajima, and Kamnitzer-McBreen-Proudfoot. We also prove a relation between BFN
Springer fibres and quasimap spaces.
