Schubert Calculus and Quantum Integrability

Explore the intersection of Schubert calculus and quantum integrability in this 52-minute lecture by Paul Zinn-Justin from the University of Melbourne. Delve into recent advancements in Schubert calculus and its newly discovered connection to quantum integrable systems. Learn how these systems provide explicit combinatorial formulae, known as "puzzle rules," for intersection numbers in partial flag varieties and their extensions to equivariant K-theory. Discover how these formulae generalize the classical Littlewood-Richardson numbers. Examine the relationship between this work and Okounkov's research on quantum integrable systems and the equivariant cohomology of Nakajima quiver varieties. Gain insights into partition function numbers, puzzles, proofs, and examples. Investigate further results in integrability, polynomials, representations, and honeycombs. This talk, part of the Asymptotic Algebraic Combinatorics 2020 series at the Institute for Pure and Applied Mathematics (IPAM) at UCLA, offers a comprehensive overview of cutting-edge research in algebraic combinatorics and its applications to quantum physics.

Intro
What is Shepard calculus
What are ecology rings
What are we interested in
Pauls role
Partition function numbers
Puzzles
Proof
Recovery
Examples
Further results
integrability
polynomials
representation
honeycombs