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Wednesday, October 30, 2013

**Abstract:** The study of fixed points of maps is a classical and important topic in geometry and topology. During this talk, we focus on the fixed points of maps in the case where manifolds admit symplectic structures and circle actions on the manifolds preserve the symplectic structures. We discuss main theorems on fixed points of symplectic circle actions and discuss techniques to study, ABBV Localization formula and Atiyah-Singer index formula.