This talk will focus on hypermultiplet moduli spaces of various N=2
supersymmetric gauge theories in (3+1)d. In the first part of the
talk, we discuss the moduli space of instantons on C2. For the
classical groups, the ADHM construction of the moduli space can be
realised on the Higgs branch of N=2 gauge theories on D3-branes
probing D7-branes. No known construction is available for exceptional
groups. We go over the computation of Hilbert series for the one
instanton moduli space and show that it is possible to count all
chiral operators on the moduli space even though a Lagrangian is not
known for exceptional gauge groups. In the second part, we discuss a
class of N=2 gauge theories on two M5-branes wrapping Riemann
surfaces. This talk will go over Hilbert series for the
hypermultiplet moduli space of such theories and show that it is
possible to count all chiral operators on the hypermultiplet moduli
space for any genus and any number of punctures of the Riemann
surface.
