Topological Quantum Field Theory

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Description

Topological quantum field theories provide a pairing between manifolds and higher categories, thus giving rise to both invariants of manifolds (e.g. Reshetikhin—Turaev and Seiberg—Witten invariants) and invariants of algebraic structures (e.g. factorization homology). They also provide toy models of quantum field theories with no nontrivial dynamics, such as the ground state of a topological order. In this course we will study a functorial approach to TQFTs concentrating on algebraic and categorical structures (categories of cobordisms, cobordism hypothesis). We will also look at several examples including the Dijkgraaf—Witten theory, ​Chern—Simons theory and A- and B-models relevant for mirror symmetry.