From boiling water to quantum gravity
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A variety of systems displays critical phenomena, from boiling water, through ferromagnets and superconductors. Remarkably, many distinct systems can behave in the same way at their critical point. In this talk I will review how we can understand this through the renormalization group, and how criticality is governed by so-called conformal field theories (CFTs). I will show how in recent years our understanding of CFTs has improved dramatically, and how this has helped understand systems ranging from boiling water to quantum gravity.