New Structures of Integrability: From Lindbladians to Non-Invertible Symmetry – September 21-25, 2026

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Organized by:

• Robert Konik (Brookhaven National Lab)
• Aditi Mitra (New York University)
• Sara Murciano (CNRS and Université Paris-Saclay -LPTMS)
• Giuseppe Mussardo (SISSA)
• Jesko Sirker (University of Manitoba)

Quantum integrability is often introduced as a story about the Yang–Baxter equation and Bethe ansatz. That story is true—and also increasingly incomplete. Over the last decade, “integrability” has started to function less like a technique confined to special Hamiltonians and more like a structural principle that organizes solvable dynamics across settings once thought hostile to exact results: dissipative (Lindblad) evolution, non-Hermitian/PT-symmetric models, and systems constrained by non-invertible/categorical symmetries. These developments are forcing a re-think of what the defining data of integrability really are (commuting charges? defects? categories? spectra of superoperators?) and which mathematical languages best capture them. This workshop will bring mathematicians and physicists together to map this expanded notion of integrability, focusing on the new algebraic and categorical structures that make exact control possible—and on the physical phenomena they now explain.