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Nathan Benjamin, USC

Title: Conformal field theory: from magnets to Hodge numbers

Abstract: I will introduce the notion of a conformal field theory (CFT), which are quantum field theories at the endpoints of renormalization group flows. CFTs show up in many areas of physics, including second-order phase transitions, string worldsheet theories, and quantum gravity in anti de Sitter space. CFTs also have applications in pure math, and can be thought of as a kind of "generalization" of geometric objects. As an example, I will show how topological invariants of certain manifolds (such as Hodge numbers) are in one-to-one correspondence with a special class of quantum states in a 2d CFT.