Conformal Field Theory (CFT) is a framework used to describe physical systems with no intrinsic length or energy scales.  CFTs have wide applicability across theoretical physics, ranging from critical points in the phase diagrams of water or magnetic materials to the low-energy dynamics of extended objects in string theory.  In this talk, I will begin by describing how CFTs can be used to understand critical phenomena.   I will then discuss recent ideas that led to tremendous progress in obtaining a quantitative understanding of various corners in the space of all possible CFTs.  I will end by discussing how CFTs can be used to describe and learn about Quantum Gravity in the presence of a negative cosmological constant.

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Recording of Professor Pufu's Talk: http://www.kaltura.com/tiny/t1zij