报告题目:Reductions and generalizations of Toda systems

报告人：李传忠教授（山东科技大学数学与系统科学学院）

报告时间：2023年3月1日13:00-14:00

报告地点：腾讯会议 676-587-002

报告摘要：In this talk, we will review a series of our studies on all kinds of reductions, and generalizations on the Toda systems, including triangular Toda hierarchy,  two-dimensional Toda hierarchy, bigraded Toda hierarchy(BTH), B(C) type Toda  hierarchy, supersymmetric Toda lattice hierarchy and finite-sized matrix-valued Toda systems. These studies contain their symmetries, Darboux transformations, tau functions and so on. We give the rational solutions of finite-sized matrix-formed Toda system which are expressed by the products of the Schur polynomials corresponding to non-rectangular Young diagrams.  Interestingly, we consider a regular solution for the (1,2)-BTH with 3-sized Lax matrix, and discuss some geometric structure of the solution from which the difference between (1,2)-BTH and original Toda hierarchy is shown.  In the case of the original Toda lattice, one can show that all the diagonal orbits have to cross the center point. However, the orbits for the (1,2)-BTH have no such restriction, but those still go through the points close to the center.

邀请人：沈守枫