In the mid-twentieth century, Coxeter groups were introduced as generalizations of reflection groups. Today, Coxeter groups arise naturally in a variety of contexts and the theory of Coxeter groups has been explored via algebraic, geometric, and combinatorial points of view. The interplay between these various perspectives provides the field with richness and depth. The purpose of this session is to report on recent advances in the theory of Coxeter groups from a combinatorial perspective with an emphasis on connections to other fields of mathematics.

This session brings together leading experts and younger researchers (including graduate and undergraduate students) to present some of the newest results in this area. The speakers' recent work includes the study of non-crossing partitions, reduced expressions, root sequences, Bruhat order, pattern avoidance, Hecke algebras, Kazhdan--Lusztig theory, Schubert calculus, cluster algebras, diagram algebras, heaps of pieces, and more.


The following is a complete list of speakers (in alphabetical order).

Schedule, Abstracts, & Slides

Below is the schedule for the special session. Click on a speaker's name to see the corresponding abstract. Clicking on the title of the talk will take you to the corresponding slides (if available).

Saturday, April 9
8:30-8:50 Warrington On the mu-coefficients of Kazhdan--Lusztig polynomials
9:00-9:20 Pohlmann A Riemann-Roch Theorem For Acyclic Heaps Of Pieces
9:30-9:50 McGregor-Dorsey Full Heaps and Minuscule Posets
10:00-10:50 Green Polytopal subcomplexes and homology representations of Coxeter groups
3:00-3:20PM Stump A uniform bijection between nonnesting and noncrossing partitions
3:30-3:50 Hanusa The enumeration of fully commutative affine permutations
4:00-4:20 Jones Abacus models for parabolic quotients of affine Weyl groups
4:30-4:50 Harper Homology representations arising from a hypersimplex
5:00-5:20 Macauley Towards a cyclic version of Matsumoto’s theorem
5:30-5:50 Chao The cyclically fully commutative elements in a Coxeter group

Sunday, April 10
8:00-8:20AM Ruff Centers of cyclotomic Hecke algebras
8:30-8:50 Cormier & Goldenberg Classification of the T-avoiding permutations & generalizations to other Coxeter groups
9:00-9:20 Daly Enumerating permutations containing few copies of 321 and 3412
9:30-9:50 Armstrong Parking Modules
10:00-10:50 Dyer Groupoids with root systems
3:00-3:20PM Denoncourt A refinement of weak order intervals into distributive lattices
3:30-3:50 Crites Pattern characterization of rationally smooth affine Schubert varieties of type A
4:00-4:20 Denton Applications of Zero-Hecke Algebras
4:30-4:50 Ripoll Geometrical enumeration of certain factorisations of a Coxeter element in finite reflection groups

Additional Information