2018-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/691792摘要：在本計劃，我們提出對critical parameter的平均場方程(曲率方程)以及SU(3) Toda system作研究，特別是在環面Eτ的方程: 另外對多個奇異點的格林函數的critical point的研究也是重點之一。方程式(1)是可積 系統，其所對應的是Treibich-Verdier potential。在KdV理論裡，這個potential有所謂的Spectral polynomial，這個 Spectral polynomials性質的探討亦是本計畫的要點之一。 <br> Abstract: In this project, we study the curvature equation and SU(3) Toda system. We also study the critical point of multiple Green functions on Eτ, which is often closely related to the bubbling phenomena of (1) and (2). Our method is to combine the analytic method and the method of integrable systems. Any solution of (1) and (2) is associated with a complex ODE. The menodromy theory would play an important role in our study, hence we also explore the algebraic side of this complex ODE.曲率方程格林函數多奇異點的格林函數奇異點譜多項式複數域的常微分方程curvature equationSU(3) Toda systemGreen functionmultiple Green functioncritical pointsODE in complex variableTreibich-Verdies potentialKdVspectral polynomial