AGT conjecture

Abstract: More than 10 years ago, I constructed representations of Heisenberg algebras and affine algebras on the homology groups of instanton moduli spaces on certain 4-manifolds. The proof was mathematically rigorous, but was not conceptually satisfactory. About two years ago, physicists, Alday-Gaiotto-Tachikawa (AGT) proposed a much larger framework, which is conceptually satisfactory, but lacks mathematical footing. I will explain their theory, and a mathematical approach towards a conjecture.