# Mod(M^4) minicourse

### August 4-7, 2022

### LECTURE NOTES

Lecture 1 (notes by Peter Huxford)

Lecture 2 (notes by Peter Huxford)

Lecture 3 (notes by Peter Huxford)

Lecture 4 (notes by Sidhanth Venkat Raman)

Lecture 5 (notes by Sidhanth Venkat Raman)

Lecture 6 (notes by Sidhanth Venkat Raman)

Lecture 9-10 (notes by Lei Chen)

Lecture 11 (notes by Lei Chen)

Typed out Lectures 1-11 (by Seung uk Jang)

### PROBLEM LISTS

Some open problems on mapping class groups of del Pezzo surfaces (by Seraphina lee)

Farb-Looijenga, Problems on mapping class groups of 4-manifolds, coming soon.

### READINGS

Scorpan, Chapter 3

Lee, Isotopy classes of involutions of del Pezzo surfaces (preprint, 2022)

Lee, The Nielsen realization problem for high degree del Pezzo surfaces (preprint, 2021)

Farb-Looijenga, The Nielsen Realization Problem for K3 surfaces (to appear in J. Diff Geom.)

Lee, Handout on maximal parabolic subgroups of O(1,9)(Z)

### EXERCISES

Exercises, 1

Exercises, 2

Exercises, 3

### Discord Server

Click the link here for group chats, administrative and mathematical questions.
I encourage people to ask questions, and also to answer them!
Group Discussion

### FROM JULY LECTURES

Lecture 1 video

Lecture 1 notes

Lecture 1 problems

Lecture 2 video

Lecture 2 notes

Lecture 2 problems

e^2=-1 proof

Lecture 3 video

Lecture 3 notes

Lecture 3 problems

### INFORMATION FOR MINICOURSE

Schedule of talks

Discussion groups