In this talk, I will focus on an infinite class of 3d N=4 gauge theories
which can be constructed from a certain set of ordered pairs of integer
partitions. These theories can be elegantly realised on brane intervals in
string theory. I will give an elementary review on such brane constructions
and introduce to the audience a symmetry, known as mirror symmetry, which
exchanges two different phases (namely the Higgs and Coulomb phases) of such
theories. Using mirror symmetry as a tool, I will discuss a certain
geometrical aspect of the vacuum moduli spaces of such theories in the
Coulomb phase. It turns out that there are certain infinite subclasses of
such spaces which are special and rather simple to study; they are complete intersections. I will mention some details and many interesting features of these spaces.