Here is a list of resources for the masterclass “recent progress on singularity analysis and applications of the mean curvature flow” (considering that the list might get a little long, having if off the official website seems best). This may be updated through the duration of the masterclass.

First, for prerequisites consider the following excellent course notes by Schulze, as well as the great survey by Bernstein:

MCF notes by Schulze
Brakke flow notes by Schulze
Shrinker survey/notes by Bernstein

Here are some relevant arXiv links for the lectures by Schulze (where the first paper linked will be the main focus, with techniques pointed to for the others).

https://arxiv.org/abs/2102.11978
https://arxiv.org/abs/2003.14344
https://arxiv.org/abs/2302.08409
https://arxiv.org/abs/2309.03856
https://arxiv.org/abs/2302.02253
https://arxiv.org/abs/2306.13191