Explore a mathematical lecture on divisorial contractions with centre a $cA_n$-singularity, presented by Erik Paemurru from the University of Miami. Delve into the simplification of existing classifications by Kawakita and Yamamoto for 3-dimensional divisorial contractions. Examine the concept of divisorial contractions with discrepancy of at least 2 to a fixed variety, focusing on $cA_n$-singularities. Discover how the existence of one such divisorial contraction implies the existence of uncountably many similar contractions. Gain insights into advanced algebraic geometry concepts and their implications in this hour-long presentation from April 1, 2022.