A classical theorem of Fatou states that a bounded holomorphic function in the unit disc $\Delta \subset \mathbb C$ has radial limits almost everywhere on $\partial \Delta$. Ever since, the problem of making sense of boundary values of holomorphic functions (in one or more variables) has been an active area of research, often yielding far-reaching theories (think Hardy spaces). In this talk I will give an overview of two classical approaches to the problem, and will outline the idea of a new construction of boundary values of holomorphic functions for domains with non-smooth boundary.

In this talk we prove a wall-crossing formula of counting invariants in the derived category of $O+O(-2)$-quiver representations. We verify the GW/DT/PT/NCDT-correspondence for the counting invariants.