What's Happening in Fine Hall

One of the central themes in geometry is that geometric objects satisfying suitable stability conditions can be parametrized by moduli spaces. Stability arises in many different contexts, often with deep and unexpected connections between seemingly unrelated notions. In this talk, we will focus on one particular notion, K-stability, which has its origins in the study of Kähler–Einstein metrics. We will discuss the algebraic theory that has developed around K-stability, with an emphasis on the construction of moduli spaces. If time permits, we will also explore some unexpected applications of this theory.