Christopher D. Hacon from The University of Utah 

Which Powers Of A Holomorphic Function Are Integrable?

Christopher D. Hacon from The University of Utah 

Let f = f(z₁, . . . , z_n) be a holomorphic function defined on an open subset P ∈ U ⊂ Cⁿ. The log canonical threshold of f at P is the largest s ∈ R such that |f|^s is locally integrable at P. This invariant gives a sophisticated measure of the singularities of the set defined by the zero locus of f which is of importance in a variety of contexts (such as the minimal model program and the existence of Kähler-Einstein metrics in the negatively curved case). In this talk we will discuss recent results on the remarkable structure enjoyed by these invariants.