XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019
VIII School on Geometry and Physics 24-28.06.2019

Alexander Zheglov

Algebraic geometric properties of spectral surfaces of quantum integrable systems and their isospectral deformations.

Quantum integrable systems, or rings of commuting partial differential operators, and their isospectral deformations admit a convenient algebraic geometric description if they are considered as subrings in a certain "universe" ring - a purely algebraic analogue of the ring of pseudodifferential operators on a manifold. This description is a natural generalization of the classification of rings of commuting ordinary differential or difference operators described in the works of Krichever, Novikov and Mumford.

Already in the case of dimension two there are significant restrictions on the geometry of spectral varieties, and therefore the question of their classification arises. I'll talk about recent results on possible types of smooth spectral surfaces. The talk is based on joint work with Vik. S. Kulikov.

Event sponsored by:
of Bialystok
University of Bialystok

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