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Duistermaat-Heckman formula and 2-dimensional Yang-Mills theory

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In 1982, Duistermaat and Heckman came up with an amazing formula which shows that for a certain type of oscillatory integrals the first two terms of the steepest descent (or stationary phase) asymptotics give the exact result for the integral. In 1992, Witten applied this idea to path integrals of the 2-dimensional Yang-Mills theory to obtain intersection pairings on the moduli space of flat connections on a 2-dimensional surface. In the talk, we'll give an elementary introduction into the Duistermaat-Heckman theory. We'll then review some of the attempts to understand Witten's path integral calculations.