Marcos Crichigno: Quantum Spin Chains and Symmetric Functions

I’ll tell you how quantum spin chains, some of the simplest quantum mechanical systems, encode a number of solutions to problems in representation theory, combinatorics, and algebraic geometry. This is revealed by the quantum integrability of the spin chains and the theory of (quantized) symmetric functions. This suggests a program to uncover the computational complexity of these computational problems, informed by the physics of 1d quantum integrable systems.