Special Events Seminar

In this thesis, we examine the nature of Temkin's canonical metrics on the pluricanonical bundles on the Berkovich analytification of an algebraic variety. These metrics encode much of the geometry of the underlying variety; for example, we show that Temkin's metric over a trivially-valued field of characteristic zero can be realized in terms of log discrepancies, which are ubiquitous invariants in birational geometry. We will discuss 3 applications of Temkin's metrics: one to the study of essential skeletons of Berkovich analytifications, another to potential theory on Berkovich curves, and finally one to the geometric P=W conjecture from non-abelian Hodge theory. Speaker(s): Matt Stevenson (UM)