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GDMSeminar: Abstracts of the Talks (2020/13)

San Vu Ngoc (Rennes)

One can hear semi-toric systems

Tuesday, November 17, 2020, 16:00 GMT

I will report on an ongoing work with Yohann Le Floch about inverse spectral theory for quantum integrable systems.

The question, adapted from the famous "Can one hear the shape of a drum?", is to fully reconstruct a semi-toric system from the joint spectrum of its quantum counterpart.

Semi-toric systems form a large class of 2D integrable systems that has been extensively studied in the last 15 years. The inverse spectral problem for these systems was proposed as a conjecture about 10 years ago. We show that the conjecture is true, by analyzing the quantum versions of all "symplectic invariants" of semi-toric systems.