The Algebraic Combinatorics Seminar

Schedule

In reverse-chronological order.

Date Speaker Title (click titles for abstract)

28 Jun. 2011 Steve Pon Affine Stanley symmetric functions and k-Schur functions for classical types.
k-Schur functions arose in the study of Macdonald polynomials, but were later found to have an important interpretation as modeling the homology Schubert basis of the affine Grassmannian of SL(n,C). In this sense, they can be generalized to other Lie types. I will present "non-commutative k-Schur functions" as elements of the nilCoxeter algebra in types A,B,C and D, as well as affine Stanley symmetric functions, which represent cohomology classes. In addition, I'll present the beginnings of a type-free description of these objects.

27 May. 2011 Chris Berg Weights of Irreducile GL_n representations.
Chris will speak on the weight theory of GL_n representations and its connections to rectangular k-Schur function expansions.

11 Mar. 2011 Mike Zabrocki Dihedral symmetry on k-Young's lattice.
Mike will speak about a dihedral symmetry on k-Young's lattice which generalizes the dihedral symmetry of Suter on Young's lattice.

4 Mar. 2011 Chris Berg Equivalence of two formulas for $k$-Schur functions.
Chris will speak on the equivalence of the two formulas previously presented in this seminar for rectangular k-Schur functions.

28 Jan. 2011 Mike Zabrocki Another formula for $k$-Schur rectangles.
Mike will speak about a formula for rectangular k-Schur functions which involves cyclic tableaux.

14 Jan. 2011 Nantel Bergeron A k-Schur formula for rectangles.
Nantel will speak on a new formula conjectured for a k-Schur function indexed by a rectangle.

12 Nov. 2010 Chris Berg Commuting $h_r$ proof from Lam's "Affine Stanley Symmetric Functions"
Chris will outline the proof from Lam's paper on why the $h_r$ commute.

5 Nov. 2010 Mike Zabrocki More Jeu de Taquin.
Mike will speak on some more guesses for a JdT rule for k-Schur functions.

29 Oct. 2010 Nantel Bergeron Jeu de Taquin for Schubert polynomials.
Nantel will speak on trying to create a JdT rule for Schubert polynomials.

22 Oct. 2010 Mike Zabrocki k-Schur functions and Jeu de Taquin, part III.
Mike will speak on some guesses for a JdT rule for k-Schur functions.

15 Oct. 2010 Nantel Bergeron How to show that a rule is good, part II.
Nantel will give conditions required for a JdT type rule to work.

8 Oct. 2010 Nantel Bergeron How to show that a rule is good.
Nantel will speak on how to verify that a JdT rule is correct.

1 Oct. 2010 Mike Zabrocki $k$-Schur functions and Jeu de Taquin, part II
Mike will speak on the k-Pieri rule and the k-Murnaghan Nakayama rule.

24 Sep. 2010 Mike Zabrocki $k$-Schur functions and Jeu de Taquin.
Mike will lead a discussion on an attempt to define Jeu de Taquin on cores and developing a Littlewood-Richardson rule for k-Schur functions.

Year	Topic
2011-2012	k-Schur functions and affine permutations
2010-2011	Littlewood Richardson rule k-Schur functions.
2009-2010	Idempotents and weakly ordered semigroups. (q,t) Catalan Numbers.
2008-2009	Littlewood-Richardson Rule, Shifted Tableaux and P-Schur functions
2007-2008	Open problems around k-Schur functions and non-commutative symmetric functions
2006-2007	Open problems
2005-2006	Cluster Algebras and Quivers
Spring 2005	Formal languages and analytic classes of functions
Fall 2004	(Quasi-) Symmetric functions in noncommutative variables and applications
Winter 2003	Crystal Bases and Representation Theory, Super-algebras, etc.
Fall 2003	Quasi-Symmetric functions and applications
Fall 2002	Crystal Bases and Representation Theory

Date	Speaker	Title (click titles for abstract)
28 Jun. 2011	Steve Pon	Affine Stanley symmetric functions and k-Schur functions for classical types. k-Schur functions arose in the study of Macdonald polynomials, but were later found to have an important interpretation as modeling the homology Schubert basis of the affine Grassmannian of SL(n,C). In this sense, they can be generalized to other Lie types. I will present "non-commutative k-Schur functions" as elements of the nilCoxeter algebra in types A,B,C and D, as well as affine Stanley symmetric functions, which represent cohomology classes. In addition, I'll present the beginnings of a type-free description of these objects.
27 May. 2011	Chris Berg	Weights of Irreducile GL_n representations. Chris will speak on the weight theory of GL_n representations and its connections to rectangular k-Schur function expansions.
11 Mar. 2011	Mike Zabrocki	Dihedral symmetry on k-Young's lattice. Mike will speak about a dihedral symmetry on k-Young's lattice which generalizes the dihedral symmetry of Suter on Young's lattice.
4 Mar. 2011	Chris Berg	Equivalence of two formulas for $k$-Schur functions. Chris will speak on the equivalence of the two formulas previously presented in this seminar for rectangular k-Schur functions.
28 Jan. 2011	Mike Zabrocki	Another formula for $k$-Schur rectangles. Mike will speak about a formula for rectangular k-Schur functions which involves cyclic tableaux.
14 Jan. 2011	Nantel Bergeron	A k-Schur formula for rectangles. Nantel will speak on a new formula conjectured for a k-Schur function indexed by a rectangle.
12 Nov. 2010	Chris Berg	Commuting $h_r$ proof from Lam's "Affine Stanley Symmetric Functions" Chris will outline the proof from Lam's paper on why the $h_r$ commute.
5 Nov. 2010	Mike Zabrocki	More Jeu de Taquin. Mike will speak on some more guesses for a JdT rule for k-Schur functions.
29 Oct. 2010	Nantel Bergeron	Jeu de Taquin for Schubert polynomials. Nantel will speak on trying to create a JdT rule for Schubert polynomials.
22 Oct. 2010	Mike Zabrocki	k-Schur functions and Jeu de Taquin, part III. Mike will speak on some guesses for a JdT rule for k-Schur functions.
15 Oct. 2010	Nantel Bergeron	How to show that a rule is good, part II. Nantel will give conditions required for a JdT type rule to work.
8 Oct. 2010	Nantel Bergeron	How to show that a rule is good. Nantel will speak on how to verify that a JdT rule is correct.
1 Oct. 2010	Mike Zabrocki	$k$-Schur functions and Jeu de Taquin, part II Mike will speak on the k-Pieri rule and the k-Murnaghan Nakayama rule.
24 Sep. 2010	Mike Zabrocki	$k$-Schur functions and Jeu de Taquin. Mike will lead a discussion on an attempt to define Jeu de Taquin on cores and developing a Littlewood-Richardson rule for k-Schur functions.