Branes, quiver gauge theories and discrete symmetries

<!--HTML-->The spaces of zero-energy configurations (moduli spaces of vacua) of supersymmetric QFTs are richly geometrically structured. Realizing quiver gauge theories as the IR descriptions of brane configurations has allowed the recent development of numerous techniques to examine this geometry. I will discuss some of these techniques and how they can be used to investigate the local geometry of moduli spaces of vacua, even if a global description is unavailable. I will also remark on how studying the manner in which these techniques change for theories with discrete symmetries can give us clues as to the phenomenology of such theories.