Gauge theory is one of the concepts at the crossroad of physics and mathematics, yielding a lot of fruitful ideas for both fields so far. Recently a powerful computational technique to evaluate the path integral has been developed for gauge theory, and it allows us to see more detailed mathematical structures lying behind it. In this talk, I’d like to talk about an emergent infinite symmetry appearing from the gauge theory moduli space, which leads to a new family of quantum algebras. I’ll also mention that such a quantum algebraic structure has a close connection to quantization of geometry.