Applications of non-commutative symmetric functions to algebraic combinatorics

点击翻译按钮获取中文摘要

In the last 25 years mathematics research has gone into the development of certain non-commutative algebraic structures. While the initial motivation for studying these algebras was simply because of their mathematical beauty, they have been shown to have many unexpected applications. I have studied various types of non-commutative objects in my past research, usually simply to discover some of their most important properties and to generalize what is known for their commutative counterparts. My current research has been to tackle some important long standing problems of algebraic combinatorics and I have found that the techniques and results developed to study non-commutative algebra have lead to important breakthroughs on seeming unrelated problems.