Vertex Models and Special Functions Seminar Fall 2021

Last Updated:

The goal of this seminar is to understand some examples in which vertex models give insight on the study of special functions, especially Macdonald polynomials.

Time and location information

Organisers: Sam DeHority, Zoe Himwich, Davis Lazowski
Time/date: Thursdays 5-6pm EST
Location: Hybrid in Math 528 / on Zoom

Please email himwich@math.columbia.edu if you would like to be on the mailing list.

Plan/references

First, we will cover necessary background on MacDonald polynomials, vertex models and DAHA, following (for instance)

Then we will focus on the box-ball system, following

Afterwards, depending on attendee interest, we will move on to several other related systems, for instance those of

Virtual attendance

This seminar will be hybrid. If you are interested in attending virtually, please let us know when you ask to be on the mailing list. (If interest from attendees at other universities is especially high, it’s possible that the seminar might move entirely online.)

List of talks

Date Talk Info
Thursday
Sep. 9
Speaker: Zoe Himwich
Title: DAHA and Macdonald Polynomials
Thursday
Sep. 16
NO TALK
Thursday
Sep. 23
Speaker: Zoe Himwich
Title: Continued
Thursday
Sep. 30
Speaker: Davis Lazowski
Title: Crystals and box-ball systems
Abstract: I will give a basic introduction to crystals and how they arise from the theory of quantum groups. Then we’ll use that to study associated dynamical systems, notably the box-ball system.
Thursday
Oct. 7
Speaker: Sam DeHority
Title: The Toda lattice and its ultradiscretization
Abstract: The Toda lattice is an example of a classical integrable system. I will describe this system and some of its solutions, then discuss its ultradiscretization, which is a certain tropical limit of the system and is related to box ball systems.
Notes: pdf
Thursday
Oct. 14
Doubleheader
First Sam continues from last week, and then Davis will speak on the following “I will briefly prove that the combinatorial R matrix describes soliton-soliton scattering”
Thursday
Oct. 21
Speaker: Zoe Himwich
Title: TBA