Hoseob Seo, On Singularities of Toric Plurisubharmonic Funcitons

In this talk, we discuss recent progresses on singularities of toric plurisubharmonic functions. First, we review the notion of Newton convex bodies of toric plurisubharmonic functions on a polydisk D(0,r) ⊂ Cⁿ. As an application, we show that the cluster points of jumping numbers of J(φ)₀ are not accumulated and give a precise characterization of the set of those cluster points. These generalize a recent result of Kim and Seo from n = 2.

On the other hand, we extends a result by Guan, which proved when toric plurisubharmonic functions of the form log(∑ |z|^a_i) have a decreasing equisingular approximation with analytic singularities. We give a criterion for the existence of a decreasing equisingular toric approximation with analytic singularities for a given toric plurisubharmonic function. This is a joint work with Jongbong An.