Lattice Theory of Noncrossing Partitions and Noncrossing Arc Diagrams - Lecture 2

Explore advanced mathematical concepts in this 47-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, then advance to detailed examination of weak order, c-Cambrian lattices, and non-crossing partitions. Conclude with contemporary research findings, open questions, and applications in representation theory and dynamics. Master essential mathematical principles through this self-contained presentation that bridges fundamental concepts with cutting-edge developments in lattice theory.