K3 surface and cubic fourfold
Student No.:10
Time:Tue & Fri 15:20-17:00, Oct.9-19
Instructor:Zheng Zhiwei  
Place:Jingzhai 112
Starting Date:2018-10-9
Ending Date:2018-10-19

This short course will be divided into four lectures:
(1) In the first lecture, I will introduce definitions and basic properties of K3 surface, hyper-Kähler manifold and cubic fourfold, and discuss relations among them.
(2) In the second lecture, I will introduce the construction of moduli space and period map of K3 surfaces and cubic fourfolds. I will talk about the global Torelli theorem.
(3) In the third lecture, I will explain how to use the previous results to realize many related moduli spaces as locally symmetric varieties. For example, the moduli of cubic surfaces is a four dimensional ball quotient. The moduli of curves of genus 4,5,6 are also included in our examples.
(4) In the fourth lecture, I will introduce the fascinating result of Mukai, that there are 13 maximal finite groups of symplectic automorphisms of K3 surfaces, and these are subgroups of the Mathieu group M23 satisfying certain property. Recently there is analogue result about cubic fourfolds, which I will try to explain about.