题 目：On two dimensional analogues of the KP hierarchy
报告人：Prof. Alexander Zheglov, Moscow State University
时 间：2019年11月1日 14：30-15：20
地 点：数学院425#
摘 要： The well-known KP hierarchy is an infinite system of nonlinear
partial differential equations, which describes, among other things, the
isospectral deformations of the rings of commuting ordinary differential
operators. In geometric terms, these deformations are described as flows
on the Jacobians of the spectral curves of such rings, which can also be
regarded as restriction of the flows defined by the hierarchy on the Sato
Grassmannian.
I will talk about the analogue of this theory in the two-dimensional case.
In this case, rings of commuting differential operators of two variables,
or more general rings of differential-difference or pseudodifferential
operators, and their isospectral deformations are considered. Deformations
are described by analogues of the KP hierarchy — the modified Parshin
hierarchies, which define flows on the moduli space of torsion-free
sheaves of a spectral surface.
