学术报告（Kanehisa Takasaki 2024.5.21）

摘要：The lattice Gelfand-Dickey hierarchy is a lattice analogue of the Gelfand-Dickey (aka generalized KdV) hierarchy.  This integrable hierarchy has an extension by an infinite number of logarithmic flows.  These flows are motivated by a possible relation with a kind of Frobenius manifolds and cohomological field theories.  The construction of the extended system resembles the extended 1D and bigraded Toda hierarchy, but exhibits several novel features as well.  Moreover, this system can be deformed to a generalization of the intermediate long wave hierarchy . This seems to explain an origin of the mysterious logarithmic flows.  This talk is based on arXiv:2203.06621 and arXiv:2211.11353.