Student Algebraic Geometry: Log Geometry

A lovely feature of algebraic varieties is that they admit compactifications. Even better, it often happens that the geometry of a compactification is influenced, or even determined, by combinatorial data, as occurs in the correspondence between toric varieties (certain compactifications of tori) and fans (combinatorial data). Log geometry is a powerful formalism for keeping track of combinatorial data at the boundary of a compactification, and since its introduction in the 1980's, it has played an important role in a wide range of topics from p-adic Hodge theory to the birational geometry of moduli spaces. The goal of the talk is to give a brief introduction to the basic language of log geometry, with no previous exposure to toric geometry assumed.