Moduli spaces in algebraic geometry

Date: Thursday 18 August 2022

Abstract

Moduli spaces are a tool used to study the classification problem in algebraic geometry, with the prototype being the moduli space of Riemann surfaces. Moduli spaces appearing in nature are rarely compact, and for a variety of reasons it is beneficial to find meaningful compactifications. An active area of current research with many fundamental open questions, is to study moduli spaces of higher dimensional algebraic varieties. Starting with the case of Riemann surfaces, I will survey some recent results in the higher dimensional setting.