Learning Seminar 10/6

Speaker: Katie Waddle

Abstract: A q-analog of a counting function is a polynomial in q that reduces to the function when evaluated at q=1. Such polynomials can keep track of extra information about the objects you are counting. We will discuss q- and q,t-analogs to the Catalan numbers, connections between them, and the statistics they encode.

Notes for the talk are here.

References:

• Chapter 3 of https://www2.math.upenn.edu/~jhaglund/books/qtcat.pdf

• https://math.berkeley.edu/~mhaiman/ftp/remarkable-qtcat/qtcat.pdf

• https://garsia.math.yorku.ca/MPWP/qtanalogs/catalan/definition.html

Speaker: David Speyer

Abstract: I'll work through what diagonal harmonics and Macdonald polynomials look like for n=2 and 3 with lots of examples.

Slides for the talk are here.