It is a well-known theorem in combinatorics that everything is counted by the Catalan numbers. These numbers are ubiquitous in mathematics, often appearing where you least expect them — such as in the HOMFLYPT polynomial of torus knots. In this talk, we’ll take a journey into algebraic combinatorics by pursuing the question: why do the torus knots know about Catalan numbers? Along the way, we’ll encounter braid groups, Hecke algebras, complex reflection groups, and more! This talk is based on a paper by Pavel Galashin, Thomas Lam, Minh-Tam Quang Trinh, and Nathan Williams.