Prof. Chen-Yu Chi
Department of Mathematics, Harvard University & NTU

Title: On some algebraic geometric aspects of the Toda systems of PDEs

Abstract:

The Toda systems on the euclidean plane or the flat two dimensional torus appear in many branches of mathematics, from applied mathematics studying tides to quantum physics. For example, the case of a single equation originated from the prescribed curvature problem in geometry and also comes from statistical physics as the mean field limits of the Euler flow. In this talk we will discuss some of its algebraic geometric aspects and a generalization to general Riemann surfaces.

Prof. Shu-Yu Hsu
Department of Mathematics, NCCU

Title: Minimizer of an isoperimetric ratio and its application to Ricci flow

Abstract:

In this talk I will prove the existence of the minimizer of an isoperimetric ratio for a metric on the plane with finite total area. I will also show how this result can be used to study the singularity properties of Ricci flow on complete $R^2$.

Prof. Chiung-Jue Sung
Department of Mathematics, NTHU

Title:Bottom spectrum and geometry

Abstract:

In this talk I will explore some structure theorems for manifolds with the weighted Poincaré inequality. This is a joint work with Nguyen Thac Dung.

.