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Recent developments on chromatic quasisymmetric functions

Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017

October 09, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Michelle Wachs (University of Miami)
Location: MSRI:
Tags/Keywords
  • chromatic symmetric functions

  • Hessenberg varieties

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

3-Wachs

Abstract

The chromatic quasisymmetric function of a labeled graph was introduced by Shareshian and myself as a refinement of Stanley’s chromatic symmetric function. We conjectured a refinement of the long standing Stanley- Stembridge e-positivity conjecture, and formulated an algebro-geometric approach to proving this refined conjecture involving Hessenberg varieties. Significant progress in this direction has recently been made by Brosnan and Chow and by Guay-Paquet. In this talk, I will discuss the connection with Hessenberg varieties, and also present some new directions, including results on generalizations to directed graphs obtained by my student Brittney Ellzey

Supplements
29701?type=thumb Wachs Notes 901 KB application/pdf Download
Video/Audio Files

3-Wachs

H.264 Video 3-Wachs.mp4 165 MB video/mp4 rtsp://videos.msri.org/data/000/029/566/original/3-Wachs.mp4 Download
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