Masters Exam

Speaker:  Chloé Napier, University of Kentucky

Title:     New Interpretations of the Two Higher Stasheff-Tamari Orders

Abstract:

In 1996, Edelman and Reiner defined the two higher Stasheff-Tamari orders on triangulations of cyclic polytopes and conjectured that they are equal. In 2021, Nicholas Williams defined new combinatorial interpretations of these two orders to make the definitions more similar. He builds upon the work by Oppermann and Thomas in the even dimensional case of giving an algebraic analog to these orders using higher Auslander-Reiten Theory. He then gives a completely new result for the odd dimensional case. In this talk, we will discuss the combinatorial interpretations of the even dimensional case and motivate the odd dimensional case and algebraic analog by example.