The Orbifold Transform and its Applications

We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the theory of permutation orbifolds is addressed, and the general results illustrated on the example of torus partition functions. Work supported by grants OTKA T047041, T043582, the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and EC Marie Curie MRTN-CT-2004-512194.