Out of curiosity . . .
What is the latest progress on the Andrews-Curtis Conjecture?
What's available online seems limited. (See the Wikipedia article linked to above.)
I found the following here:
Here ZC is the Zeeman Conjecture and PC is the Poincaré conjecture.
My Background: I did an MPhil in combinatorial group theory. It ended in 2022. See my profile for more.