报告人：聂兆虎（犹他州立大学）
时间：2026年5月29日14:30-15:30
地点：数院新楼308
Following many authors, I will define a Toda system on a Riemann surface as a sequence of Kähler forms whose Ricci forms are linear combinations of the Kahler forms using the Cartan matrix of a simple Lie algebra. The simplest case is the Liouville equation, and as such, Toda systems are generalizations of Kähler-Einstein metrics to sequences of metrics on compact complex manifold, including algebraic curves. If we don't allow singularities for the Ricci forms, one can show that the curve must be CP^1, and the solutions are classified in our previous work [KLNW]. Those solutions are special cases of the so-called toric solutions of Toda systems, where the monodromies of the solutions land in a maximal torus of the maximal compact group of the complex Lie group. We show how to construct general toric solutions of Toda systems on a general Riemann surface using special 1-forms of the third kind. This is a joint work in progress with Bin Xu.
