Learning Seminar 9/22

Speaker: Sunita Chepuri

Abstract: We begin by combinatorially defining Macdonald polynomials and discussing their relationship to other symmetric functions. We will then define the nabla operator and state the Shuffle Theorem. If time permits, we will explore the relationship between Macdonald polynomials and the ring of diagonal coinvariants.

Notes for the talk are here.

References:

• Chapter 2, Chapter 6 (page 91-92), and Appendix A (page 123-125) of https://www2.math.upenn.edu/~jhaglund/books/qtcat.pdf

• https://www.symmetricfunctions.com/macdonaldH.htm#macdonaldHProperties

• https://www.ams.org/journals/bull/2020-57-01/S0273-0979-2019-01672-3/S0273-0979-2019-01672-3.pdf