Shoemaker Lecture Series with Dr. Christopher Halcon, "Which Powers of a Holomorphic Function are Integrable?"

Lecture III of the Fall 2026 Shoemaker Lecture Series, featuring renowned mathematician Dr. Christopher Hacon of the University of Utah. Hacon is a leading expert in algebraic geometry, a member of the National Academy of Sciences and a Fellow of the Royal Society. He also shared the 2018 Breakthrough Prize in Mathematics for his contributions to birational algebraic geometry. Abstract: Let f = f(z1, ..., zn) be a holomorphic function. The log canonical threshold of f at P is the supremum of the real numbers s ≥ 0 for which |f|−2s is locally integrable near P. This invariant gives a sophisticated measure of the singularities of the zero locus of f. It is important in a variety of contexts, including the minimal model Program and the study of Kähler-Einstein metrics. In this talk we will discuss recent results on the remarkable structures enjoyed by these invariants. Visitor parking on campus requires payment through the ParkMobile app , a parking meter or a daily permit via ParkUToledo. Visit the ParkUToledo website for more information.