- This event has passed.
A polyhedral view of refined q-t Catalan numbers (Max Hlavacek, Pomona College)
September 25 @ 4:15 am - 5:30 pm
Title: A polyhedral view of refined q-t Catalan numbers
Speaker: Max Hlavacek Assistant Professor of Mathematics and Statistics department, Pomona College, Claremont
Abstract: Many problems in algebraic combinatorics have geometric objects lurking in the background, and bringing these objects forward can shed some light on the original problem. We begin with an introduction to polyhedral cones and their connection to multivariable generating functions. Then, we pivot and introduce Catalan-Minggatu numbers and some of their generalizations, including refined q-t Catalan numbers, first introduced by Xin and Zhang in 2022. Finally, we take a look at the polyhedral cones underlying these objects and see how these geometric objects can give us insight into open problems about refined q-t Catalan numbers.
Bio: Max Hlavacek is a Visiting Assistant Professor in the mathematics and statistics department at Pomona College. Previously, they were a graduate student at UC Berkeley and an undergraduate student at Harvey Mudd College. They are interested in problems in enumerative geometric combinatorics, particularly concerning discrete volumes of polytopes. They love thinking about math with others, and especially enjoy learning about the interplay between polyhedral objects such as cones and polytopes and their friends’ and collaborators’ mathematical interests.
The talk is based on joint work with Matthias Beck, Mitsuki Hanada, John Lentfer, Andrés R. Vindas-Meléndez, and Katie Waddle.
