My research in string theory and quantum field theory has primarily involved understanding their implications for modern mathematics. Most recently, I have studied various aspects of a four-dimensional analogue of Chern-Simons theory that encapsulates various notions of integrability found in mathematical physics. In particular, I have shown that there exists a three-dimensional analogue of the Wess-Zumino-Witten model that describes edge modes of the Chern-Simons theory, but seems to capture much of the bulk physics.