GRK 1133: Geometry and Analysis for Symmetries

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The analysis of systems with symmetries involves a number of different mathematical fields from representation theory and harmonic analysis, the theory of integral transformations, symplectic/complex and non-commutative geometry as well as infinite dimensional differential geometry and quantisation. Even though many central questions in the analysis of symmetries are still open, their study has produced a wealth of deep results with very diverse applications to fields such as partial differential equations, mathematical physics, number theory, ergodic theory, complex analysis, and index theory.