This is Sota Asai. I have the following problem related to my minicourse. Let $K$ be an algebraically closed field. Consider the path algebra $A:=KQ$, where the quiver $Q$ has three vertices $1,2,3$ and three arrows $\alpha \colon 1 \to 2$, $\beta \colon 1 \to 2$ and $\gamma \colon 2 \to 3$. Then, describe the non-rigid region $\mathsf{NR}$ and the purely non-rigid region $R_0$ of the real Grothendieck group $K_0(\operatorname{proj} A)_\mathbb{R}$ as explicitly as possible. This path algebra appears in Example 5.8 of my paper "The wall-chamber structures of the real Grothendieck groups", where the wall-chamber structure on $K_0(\operatorname{proj} A)_\mathbb{R}$ is partially depicted. The definitions of the non-rigid region and the purely non-rigid region are written in Section 6 of our preprint "Semistable torsion classes and canonical decompositions" with Osamu Iyama. I will talk about them in the last lecture of my minicourse if time permits. I am sorry for that there is insufficient information in this post. I will add some useful references later.