Speaker:  Sam Hsiao
Title:   Peaks, shuffles, and multigraded Hopf algebras
Time: 2:30 PM, Monday, November 30, 2009
Place:  Malott 206

Abstract:  Quasisymmetric functions are useful for investigating various types of shuffles in which we only want to keep track of the descent sets of the underlying permutations. After reviewing some results linking quasisymmetric functions to shuffling, I will discuss how peak sets enter the story in the context of "up-down" shuffles. This leads naturally to the study the peak subalgebra. I will present various multigraded generalizations and refinements of the peak algebra, and discuss the relevance of these algebraic objects to the study of certain Markov chains based on wreath products with the symmetric group.

November 19, 2009