|Date||Apr 18, 2023|
The classical coinvariant ring Rn is an important representation with significant connections to combinatorics, representation theory, and algebraic geometry. Over the last 30 years, several generalizations of coinvariant rings and their structures have been studied. In this talk, I will provide a brief overview of the history of coinvariant rings and introduce two specific examples: Garsia-Haiman modules and diagonal coinvariants. Additionally, I will discuss recent findings that connect these two examples. My talk is based on collaborative work with Donghyun Kim and Seung Jin Lee.