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Title: Physics in 2D – from the Kosterlitz-Thouless Transition to Topological Insulators

Abstract: A survey of “Physics in 2D” is presented: The Mermin-Wagner-McBryan-Spencer Theorem is recalled. Crucial ideas (among others, energy-entropy arguments for defects) in a proof of existence of the K-T transition in the 2D classical XY model are highlighted. Subsequently, the Topological-Field-Theory Approach to the Fractional Quantum Hall Effect and to 2D time-reversal invariant Topological Insulators with chiral edge spin-currents (1993) is described. The roles of anomaly cancellation, of braid statistics and of bulk-edge duality in the analysis of such systems are explained. Some general conclusions about Physics in two dimensions are outlined.