Moduli Spaces of Instantons and Integrable Systems - From Calogero-Moser to DELL Systems

Explore a mathematics seminar lecture that delves into the intricate connections between generalized equivariant cohomology theories of instanton moduli spaces on \mathbb{C}^2 and prominent integrable systems including Calogero-Moser, Ruijsennars-Schneider, and DELL. Learn about θ-transforms of qq-characters vev's and their relationship to quantum spectral curves, followed by an examination of orbifolded versions involving affine Laumon spaces. Discover how these concepts lead to new formulations of Lax matrices and their eigenvectors, while also understanding the quantum-classical duality between trigonometric degenerations and corresponding spin chains, as well as their spectral duality implications.