Vertex Models and Special Functions Seminar Fall 2021

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)

• Alcove walks, Hecke algebras, spherical functions, crystals and column strict tableaux, Ram
• Algebraic analysis of solvable lattice models, Jimbo–Miwa
• Double Affine Hecke Algebras, Cherednik

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

• Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry, Inoue–Kuniba–Takagi

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

• From Multiline Queues to Macdonald Polynomials via the Exclusion Process, Corteel–Mandelshtam–Williams
• Coloured Stochastic Vertex Models and their Spectral Theory, Borodin–Wheeler
• Nonsymmetric Macdonald Polynomials via Integrable Vertex Models, Borodin–Wheeler

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