My research topic is a mathematical study of gauge theories, which have their origin in mathematical physics. In particular, I study homology groups of various moduli spaces appearing in gauge theories, using a technique called geometric representation theory. Not only can this study be considered an analysis of gauge theories, it also sheds an interesting new light on representation theory, as I obtain familiar objects like Kac-Moody Lie algebras and their quantum analogue in a very different manner than usual. Recently I give a mathematically rigorous definition of Coulomb branches of 3d supersymmetric gauge theories using this method, and study their properties and representation theory of their noncommutative deformations (quantization).