** Speaker:** Peter Tingley, Loyola University Chicago

** Title:** Crystal combinatorics from Lusztig's PBW bases

** Abstract: **
In the early 1990s both Lusztig and Kashiwara developed a theory of canonical bases for certain
Kac-Moody algebras (called the canonical basis by Lusztig and the global crystal basis by
Kashiwara). The approaches are pretty different, and the work went in different directions: Lusztig
used geometry and ultimately categorification, while Kashiwara went in a more combinatorial
direction, developing the theory of crystals.
In this talk we will discuss an alternate reality where Lusztig's approach, in particular his theory
of PBW bases, was used to develop crystal combinatorics (in finite type). This gives new insights
into such classical combinatorial objects as Young tableaux, as well as giving rise to more exotic
combinatorics. This is joint work with Ben Salisbury and Adam Schultze.