学术报告

报告题目：Combinatorial Hopf algebras of trees

报告人：李舒啸 博士（加拿大约克大学）

报告时间：11月7日（星期四） 16:00-17:00

报告地点：数学与统计学院学术报告厅（25教14楼）

参加人员：教师，研究生，本科生

摘要：Hopf algebra is a vector space H, with a product operation m: H x H -> H and a coproduct operation Delta: H -> H x H that satisfy certain compatibility axioms. Hopf algebras play a central role in algebraic combinatorics. We illustrate this with the example of symmetric group representations and the symmetric functions. We then discuss other classical combinatorial Hopf algebras including quasi-symmetric functions, non-commutative symmetric functions, Loday-Ronco Hopf algebra of binary trees and Malvenuto-Reutenauer Hopf algebra of permutations. These Hopf algebras are closely related to each other via projections and embeddings that are compatible with their underlying posets. We generalize them to planar trees, labelled trees and parking functions, and study their algebraic structures, self-duality and antipodes. Lastly, we will talk about Schur's Q functions and peak algebra.

报告人简介：李舒啸，加拿大约克大学博士，约克大学/香港浸会大学博士后，研究方向为基础数学，主要研究代数组合学中的Hopf代数，研究成果相继发表在Electron. J. Combin.，Ann. Comb.等重要期刊上面。