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June 5, 2021, 2-5pm Hong Kong time.
Tencent Meeting link.
Time: 2-2:40pm
Title: Refined Finite-dimensional Reduction Method and Applications to Nonlinear Elliptic Equations
Speaker: Weiwei Ao, Wuhan University
Abstract: I will talk the refined finite dimensional reduction method and its application to nonlinear elliptic equations. We use this refined reduction method to get optimal bound on the number of interior spike solutions of the singularly perturbed Neumann problem. I will also talk about spike solution concentrating on boundary segment.
Time: 2:45-3:25pm Title: Generalized Adler-Moser polynomials and multiple vortex rings for the Gross-Pitaevskii equation Speaker: Yong Liu, USTC Abstract: We construct new finite energy traveling wave solutions with small speed for the three dimensional Gross-Pitaevskii equation. These solutions have the shape of 2n + 1 vortex rings, far away from each other. Among these vortex rings, n + 1 of them have positive orientation and the other n of them have negative orientation. The location of these rings are described by the roots of a sequence of polynomials， which can be regarded as a generalization of the classical Adler-Moser polynomials. Time: 3:30-4:10pm Title: Local mass and a priori estimate for singular Toda system Speaker: Wen Yang, CAS Wuhan Abstract: In this talk, we will discuss the local masses of Toda system with n>=2. By using Pohozaev identity, the monodromy theory from complex ODE and some recent work by Eremenko-Gabrielov-Tarasov, we are able to determine the local masses for the system and it turns out that the local masses are closely related to the element in the Weyl group of the corresponding Lie algebra. Based on this quantization result, the a priori estimate and some existence results of this system are obtained. Time: 4:15-4:55pm Title: Singularity formation for the nonlocal harmonic map flow Speaker: Youquan Zheng, Tianjin University In this talk, I will introduce some new results on the singularity formation of nonlocal harmonic map flow as well as its relation with a classical geometrical problem. |