Lattice Theory of Noncrossing Partitions and Noncrossing Arc Diagrams - Lecture 3

Explore advanced mathematical concepts in this 57-minute lecture from the Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability" at the Erwin Schrödinger International Institute. Delve into the combinatorics of finite lattices and their relationships with Coxeter-Catalan combinatorics, representation theory, and dynamics, with particular emphasis on the connection between noncrossing partitions and c-Cambrian lattices. Begin with foundational concepts and definitions accessible to those with basic poset knowledge, progressing through the weak order and c-Cambrian lattices, and culminating in cutting-edge research findings and open questions in representation theory and dynamics. Master essential mathematical tools and theorems while discovering the intricate interplay between various mathematical structures in this self-contained advanced mathematics lecture.