The seminar is on Wednesdays at 3:45 pm
in Bradley 103.
December 1, 2004
Louis
Shapiro,
Dartmouth (Howard)
Title: The Riordan Group, second installment
The topics will be open problems, dot diagrams, productions
matrices, and Emeric Deutsche's differential equations.
November 17, 2004
Mark Skandera,
Dartmouth
Title:
Zazhdan-Lusztig immanants and products of matrix minors
Abstract: In 1990,
Goulden and Jackson conjectured interesting
nonnegativity properties of polynomials in n^2 variables which are
related
to representations of S_n. Greene, Haiman, and Stembridge immediately
and
independently proved some of these conjectures, with Haiman using the
Kazhdan-Lusztig basis of the group algebra of S_n. More than a decade
later, Fallat, Gekhtman and Johnson observed that very different
polynomials posess some of the same properties. We will apply Haiman's
methods to these polynomials to generalize the results of Fallat,
Gekhtman
and Johnson. The presentation will focus on the combinatorial statement
of this generalization, deemphasizing some of the gory details in the
definition of the Kazhdan-Lusztig basis.
November 3, 2004
Louis Shapiro,
Dartmouth (Howard)
Title: The Riordan Group II
The topics for this talk are
1. A brief review of the Colloquium talk
2. The Riordan group for exponential generating functions
including examples, subgroups, and inversions
3. The Stieltjes transform.
October 27, 2004
Rosa Orellana,
Dartmouth
Title: Symmetric functions and characters
of S_n
Abstract:
I will discuss an open problem on the characters of the
symmetric group.
The talk will build on last week's talk by Mark; however, I will
shortly
review all the necessary background in case you missed last week.
This talk is accessible to undergraduates.