Combinatorial Representation Theory Seminar

This seminar meets Wednesdays at 4:15 PM in 383N during Fall 2013.

Wednesday, September 25	Persi Diaconis	Introduction to Symmetric Polynomials
Wednesday, October 2	Daniel Bump	Introduction to Macdonald Polynomials
Wednesday, October 9	Angela Hicks	The Modified Macdonald Polynomials
Wednesday, October 16	Angela Hicks	The Diagonal Harmonics
Wednesday, October 23	Angela Hicks	Nabla and the Modified Macdonald Polynomials
Wednesday, October 30	Daniel Litt	Introduction to the Hilbert Scheme of Points
Wednesday, November 6	Daniel Litt	Macdonald Polynomials and the Hilbert Scheme
Wednesday, November 13	Adriano Garsia	($q$,$t$)-combinatorics and Macdonald Polynomials
Wednesday, November 20	Li-Cheng Tsai	A Probabilistic View of Macdonald Polynomials
Wednesday, November 27	No Seminar
Wednesday, December 4	Daniel Bump	Macdonald Polynomials and the six-vertex model

Papers

• A New Class of Symmetric Functions by Macdonald
• Schur Functions: Theme and Variations by Macdonald.
• Duane, Garsia and Zabrocki, A new DINV arising from the two part case of the Shuffle Conjecture. Angela recommends Section 2 for its discussion of the Plethystic notation.
• Garsia and Tesler, Plethystic formulas for Macdonald $q$,$t$-Kostka coefficients. Adv. Math. 123 (1996), no. 2, 144–222 also discusses this notation.
• Haiman, Macdonald Polynomialls and Geometry discusses the plethystic notation and the geometry of the Hilbert scheme as related to the Schur positivity and the diagonal harmonics that Angela spoke about on October 9.
• The $q$,$t$-Catalan Numbers and the Space of Diagonal Harmonics by Jim Haglund.