Quantum footprints of Liouville integrable systems

Abstract

We discuss the problem of recovering geometric objects from the spectrum of a quantum integrable system. In the case of one degree of freedom, precise results exist. In the general case, we report on the recent notion of good labellings of asymptotic lattices.

11 pages. This text reports on a talk given by the author at the QMath14 conference in Aarhus. To appear in Reviews in Mathematical Physics

References in corpus (4)

• Integrable systems, symmetries and quantization
• Vanishing Twist near Focus-Focus Points
• Vu Ngoc's Conjecture on focus-focus singular fibers with multiple pinched points
• Semitoric systems of non-simple type