Algebraic Combinatorics - Carolina Benedetti

Thursday, March 10, 2016 2:00 pm - 2:00 pm EST (GMT -05:00)

Title: Hopf algebras, colorings and simplicial complexes

Speaker: Carolina Benedetti
Affiliation: York University
Room: MC 6486

Abstract: Inspired by the theory pioneered by Stanley's chromatic  
symmetric function and its connection to Hopf algebras, we will see  
how abstract simplicial complexes can be endowed naturally with a  
combinatorial Hopf structure that gives rise to chromatic generating  
functions. Using principal specializations on these generating  
functions we obtain certain combinatorial identities involving acyclic  
orientations related to the complexes. We will explore different  
expansions in terms of symmetric functions of these chromatic  
functions and derive certain information of the complex out of it.
  If time permits, we will discuss work in progress aiming to derive  
the analogous of Shareshian-Wachs "chromatic quasisymmetric functions"  for simplicial complexes.
This is joint work with Josh Hallam and John Machack.