For a projective log canonical pair (X,B) of log general type, the set of volumes vol(X,K_X+B) satisfies the Descending Chain Condition (DCC) when the coefficients of the boundary divisor lie in a given DCC set. A natural further direction is to investigate the fine distribution of these volumes, particularly the structure of their (iterated) accumulation points.

In this talk, I will survey known results on the accumulation behavior of volumes and present recent progress on their iterated accumulation structure. Through explicit geometric constructions, we prove that even in the simplest case where the coefficient set is {0}, the local accumulation complexity of the volume set can be infinite. Our approach builds upon earlier work by Blache and Alexeev–W. Liu.