The classification of finite groups acting on complex K3 surfaces

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Symmetry has fascinated humans since thousands of years. Besides its intrinsic aesthetics, symmetry plays a central role in Physics. It determines which quantities, e.g. energy and momentum, of a system are preserved or what the elementary particles of our universe are. The mathematical theory of symmetry has changed our everyday lives. Secure communication in the Internet, e.g. in online shopping, is provided by algorithms based on the symmetry of elliptic curves. These are one dimensional objects described by polynomial equations. Possible generalizations of elliptic curves are so called K3 surfaces. This project aims at classifying their finite symmetries.