Abstract: Kazhdan-Lusztig polynomials are fascinating! In the 80s Lusztig and Dyer independently noticed that the Kazhdan-Lusztig polynomial for a pair x,y of elements in a Coxeter group appears to only depend on the isomorphism type of the interval [x,y] in Bruhat order. This statement became known as the combinatorial invariance conjecture. I will review this conjecture, and discuss what is known. I will present a conjecture which should lead to a proof when W is the symmetric group.
Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.