Algebraic combinatorics learning seminar: Solvable lattice models in combinatorics

Fall 2026
Organizers: Grant Barkley, Thomas Lam, Yelena Mandelshtam, Rui Xiong

A learning seminar on solvable lattice models and their applications to Schubert calculus, quantum groups, and quiver varieties. Our goal is to understand (some subset of) the following three papers by Allen Knutson and Paul Zinn-Justin:

• [1]: Schubert puzzles and integrability I: invariant trilinear forms
• [2]: Schubert puzzles and integrability II: multiplying motivic Segre classes
• [3]: Schubert puzzles and integrability III: separated descents

A preliminary syllabus for the seminar can be found here.

Location:
East Hall 4088

Time:
Wednesdays 2:30-3:30pm

Background:

• [4]: Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
• [5]: Integrability and combinatorics

Schedule

Date	Topic	Speaker	Notes
September 16	Introductory talk	Rui	Notes
September 23	Fock space	Dawei	Notes
September 30	Plane partitions	Yucong	Notes
October 7	Six-vertex model I	Bailee	Notes
October 14	Nakajima quiver varieties in type A	Raj Gandhi	Notes
October 21	Six-vertex model II	Junaid	Notes
October 28	Loop models	Yucong
November 4	Temperley-Lieb algebra	Paul
November 11	??	??
November 18	??	Rui
December 2	??	Dima
December 9	??	Allen