# Automorphisms of K3 surfaces and their applications

## TL;DR

This survey explores automorphisms of K3 surfaces and related log rational surfaces, discussing their properties and applications within integrable systems, based on a talk given in 2018.

## Contribution

It provides a comprehensive overview of automorphisms of K3 surfaces and their applications, including log del Pezzo and log Enriques surfaces, consolidating recent developments.

## Key findings

- Summarizes key properties of automorphisms on K3 surfaces.
- Highlights applications in integrable systems.
- Reviews classifications of related log rational surfaces.

## Abstract

This paper is a survey about $K3$ surfaces with an automorphism and log rational surfaces, in particular, log del Pezzo surfaces and log Enriques surfaces. It is also a reproduction on my talk at "Mathematical structures of integrable systems and their applications" held at Research Institute for Mathematical Sciences in September 2018.