Shi-like and Catalan-like Deformations for Restricted Reflection Arrangements

This 42-minute conference talk by T. Douvropoulos explores Shi-like and Catalan-like deformations for restricted reflection arrangements as part of the Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in February 2025. Discover how the Shi and Catalan arrangements function as deformations of the braid arrangement with notable numerological and structural properties, where regions can be labeled by parking functions and trees, and natural statistics on dominant regions determine Whitney numbers for the lattice of noncrossing partitions. Learn about recent work that generalizes these constructions to restrictions A^X of reflection arrangements A on arbitrary flats X, exploring how these simple arrangements, though not crystallographic, allow for free deformations with similar properties to the Catalan and Shi cases. The presentation connects these concepts to the representation theory of parking spaces and rational Cherednik algebras, the combinatorics of W-noncrossing partitions, and ramification formulas associated with the braid monodromy of Weyl groups W.