Kai Xu a graduate student in the Math Department at Harvard University. He is advised by Professor Shing-Tung Yau. He is generally interested in the geometry of quantum field theory and string theory. Currently, he is working to understand the relation between higher Teichmuller space, opers and W-algebra, motivated by the AGT correspondence for supersymmetric gauge theory. More precisely, AGT correspondence predicts that compactification of six dimensional (2,0) SCFT reveals deep connection between two dimensional Toda field theory and four dimensional N=2 supersymmetric gauge theory, and the correspondence between the mathematical structures on both sides (for example, conformal blocks and partition functions) still remain open.