The classification of finite groups acting on complex K3 surfaces

几千年来，对称性一直令人类着迷。除了其内在的美学，对称性在物理学中也发挥着核心作用。它决定了一个系统的哪些量，例如能量和动量是保持不变的，或者我们宇宙中的基本粒子是什么。对称的数学理论已经改变了我们的日常生活。互联网中的安全通信，例如在线购物中，由基于椭圆曲线对称性的算法提供。这些是用多项式方程式描述的一维物体。椭圆曲线的可能推广是所谓的K3曲面。本课题旨在对它们的有限对称性进行分类。

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.