Instructor: Prof. Nantel Bergeron
Email: bergeron@yorku.ca
Application Deadline: January 17th, 2022
Lecture Times: Tuesdays and Thursdays | 1:00 pm - 2:30 pm 
Course Dates: January 11th - April 7th, 2022
Mid-Semester Break: February 21st - 25th, 2022
Prerequisites: Students will be expected to have a strong background in linear algebra, and some mathematical maturity
Grading: Students will be expected to attend lectures, work on assignments and do some short presentations. The final grade will be based on a combination of these activities.
Registration Fee: PSU Students - FREE | Other Students - $100 

Course Overview

What is a Hopf algebra? (algebra, coalgebra, antipodes); Review of symmetric functions as Hopf algebra; Zelevinsky’s structure theory of positive self-dual Hopf algebras; Quasisymmetric functions and P-partitions; Polynomial generators for QSym and Lyndon words; Aguiar-Bergeron-Sottile theory of characters and universal property of QSym; Malvenuto Reutenauer Hopf algebra of permutation; and further topics (Including Hopf algebra of trees and more as time allows). 

Main Reference
Hopf Algebras in Combinatorics, Darij Grinberg, Victor Reiner, arXiv:1409.8356 .

Course Description

From the excellent reference: https://arxiv.org/abs/1409.8356 [arxiv.org] : 1. What is a Hopf algebra? (algebra, coalgebra, antipodes) 2. Review of symmetric functions as Hopf algebra 3. Zelevinsky’s structure theory of positive self-dual Hopf algebras 5. Quasisymmetric functions and P-partitions 6. Polynomial generators for QSym and Lyndon words 7. Aguiar-Bergeron-Sottile theory of characters and universal property of QSym 8. Malvenuto-Reutenauer Hopf algebra of permutation 9. Further topics (Including Hopf algebra of trees and more as times allow)