几何方程小型会议日程-2019-05(简洁).docx

几何方程小型会议日程-2019-05(简洁)
几何方程小型会议日程-2019-05(简洁)
几何方程小型会议日程-2019-05(简洁)
Mini-Workshop on Geometric PDEs
, 华东师范大学
Title: Concentration in nonlinear Schr? dinger equation
Abstract: In this talk we shall talk about the concentration phenomena in nonlinear
Schr? dinger equation. Finite dimensional reduction method and infinite dimensional reduction method will be introduced.
敖轻轻，武汉大学
Title: Periodic Maxwell-Chern-Simons vortices with concentrating property
Abstract: In order to study electrically and magentically charged vortices in fractional quantum Hall effect and anyonic superconductivity, the Maxwell-Chern-Simons (MCS) model was introduced by [Lee, Lee, Min (1990)] as a unified system of the classical Abelian-Higgs model (AH) and the Chern-Simons (CS) model. First we improve and complete the (CS) limit result of (MCS) model without any restriction on either a particular class of solutions, the number of vortex points, or the Chern-Simons parameter. The most important step for this purpose is to derive the relation between the Higgs field and the neutral scalar field. Our (CS) limit result also provides the critical clue to answer the open problems raised by [Ricciardi,Tarantello (2000)] and [Tarantello (2004)], and we succeed to establish the existence of periodic Maxwell-Chern-Simons vortices satisfying the concentrating property.