|Colloquium, 國立成功大學數學系 林育竹教授|
Thursday, September 23, 15:10—17:00 數學系3174
|Colloquium, 國立陽明交通大學應用數學系 黃信元教授|
Thursday, September 30, 16:10—17:00 數學系3174
Title: An Introduction to Inverse Scattering Transform
It is an introductory talk on inverse scattering transform method in integrable systems. The inverse scattering transform (IST) is a method for solving some non-linear partial differential equations. The method is a non-linear analogue of the Fourier transform. This method was first introduced by Gardner-Greene-Kruskal-Miura for the Korteweg–de Vries equation, and soon extended to the nonlinear Schrodinger equation, sine-Gordon equation, the Toda lattice equation and so on. In this talk, I will introduce the IST for Kdv and Toda Lattice, and the connection between IST and Riemann-Hilbert problem.
|Colloquium, 國立中正大學數學系 張瑞恩教授|
Thursday, October 7, 16:10—17:00 數學系3174
Title: Stability of Regular Shrinkers in the Network Flow
Abstract:In this talk, I'll present the problem I'm working on and some partial results.
In the network flow, singularities may form. They can be described as self-similar shrinking solutions called regular shrinkers. An important problem is that if we perturb the initial
network, will the new network flow to the same singularity? All network with 2 or more enclosed regions can be perturbed away. Therefore, the problem reduces to the network
with less than 2 enclosed regions. There are infinitely many of them and they are completely classified. Here, I use the entropy argument as in Colding and Minicozzi's work to show that
the 4-ray star, the 5-ray star, the fish, and the rocket can be perturbed away.