Lattice Theory of Noncrossing partitions and Noncrossing arc diagrams

Emily Barnard (DePaul U, Chicago)

Feb 20. 2025, 15:00 — 15:45

In this series of lectures we will explore the combinatorics of finite lattices, their connection to Coxeter-Catalan combinatorics, representation theory, and dynamics. We will play special attention to the interplay between the lattice of noncrossing partitions and c-Cambrian lattices. 

My lectures will be self-contained. While some basic familiarity with posets will be helpful, I will not assume knowledge about lattices and their properties. We will begin with a survey of helpful definitions, useful theorems/tools, and classical constructions. Our second lecture will focus directly on the lattice theory of the weak order, c-Cambrian lattices, and non-crossing partitions.

Finally, we will end with very recent results and open questions, including connections to representation theory and dynamics.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Files:
Slides
Associated Event:
Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability (Workshop)
Organizer(s):
Adrian Celestino Rodriguez (TU Graz)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
James Mingo (Queen's U, Kingston)
Martin Rubey (TU Vienna)
Eleni Tzanaki (U of Crete)
Yannic Vargas (CUNEF U, Madrid)