K3曲面是一类重要的曲面, 被应用于研究代数几何里的许多问题. Salem数是一类特别的代数整数, 出现在多个数学领域中. 在2002年, McMullen观察到K3曲面的自同构和Salem数有一种密切的关系. 这种关系已经被广泛地研究, 但是仍然有诸多著名的问题待解决. 本项目将围绕这种关系研究几个问题, 主要研究内容有：1. 确定Enriques曲面的自同构的最小正拓扑熵; 2. 以Salem数为切入点，研究超奇异K3曲面的自同构和非射影K3曲面的自同构之间的关系; 3. 借助于椭圆纤维化，研究奇异K3曲面的自同构和Salem数的关系. 本项目的研究不仅有助于加深人们对K3曲面和Salem数的关系的理解, 而且有助于促进代数几何、数论、复动力系统、群论等多个领域的交叉融合.

K3 surfaces are important surfaces, and have been used in the study of many problems in algebraic geometry. Salem numbers are a special kind of algebraic integers, and have appeared in many areas in mathematics. In 2002, McMullen observed that automorphisms of K3 surfaces and Salem numbers are closely related. This relation has been studied from many different aspects, but there are still many famous unsolved problems. This project studies several problems which are very closely related to this relation, and the themes are the followings: 1. to determine the minimum of positive topological entropies of automorphisms of Enriques surfaces; 2. to study the relation between automorphisms of supersingular K3 surfaces and automorphisms of non-projective K3 surfaces via Salem numbers; 3. to study the relation between singular K3 surfaces and Salem numbers with the help of elliptic fibrations. The study of this project will not only help to deepen the understanding of the relation between K3 surfaces and Salem numbers, but also help to enhance the interactions among algebraic geometry, number theory, complex dynamics, group theory and so on.