时间：2023年9月22日8:50-17:30

地点：数学院南楼N202

报告1：The PML-method for a scattering problem for a local perturbation of an open periodic waveguide（张汝明，柏林工业大学）

Abstract: In this talk, we study the convergence of the PML method to approximate wave propagating in an open periodic waveguide. Different from the scattering problem with periodic surfaces, the existence of propagating modes makes things challenging. We apply a complex contour integral method to deal with the difficulty. Finally an exponential convergence of the PML method is proved.

报告2：New elliptic constraints for binary black holes collision in numerical relativity（冯学锋，北京雁栖湖应用数学研究院）

Abstract: A new geometric definition of angular velocity of a rotating black hole is proposed and a compressible fluid flow picture for the angular velocity is constructed.  A new set of coupled elliptic equations is then written down as the constraint equations for the vacuum Einstein field equations to describe the dynamics of binary black holes considered in gravitational wave detection.  Spectral method is then employed to solve the elliptic equations.

报告3：Stability of plane ideal flows with concentrated vorticity（王国栋，哈尔滨工业大学）

Abstract: In 1995, Elcrat and Miller constructed a family of steady Euler flows with concentrated vorticity in a 2D bounded domain. In this talk, we will report our recent progress on the nonlinear stability of these flows.

报告4：Vacuum free boundary problems in ideal compressible MHD（王涛，武汉大学）

Abstract: We present the joint works with Paolo Secchi and Yuri Trakhinin on the local well-posedness of vacuum free boundary problems in ideal compressible magnetohydrodynamics with or without surface tension.

报告5：The critical points of Robin function and Kirchhoff-Routh function（罗鹏，华中师范大学）

Abstract: The properties of Robin function and Kirchhoff-Routh function play a very basic role in the study of elliptic equation, fluid mechanics, dynamic system, geometry and topology, etc. However, the property of the critical point is still unclear for large class of domains. In this talk, we give some results on the number of non-degeneracy of critical pints of Robin function and Kirchhoff-Routh function. These are joint work with Francesca Gladiali, Massimo Grossi and Shusen Yan.

报告6：Dynamics of competitive systems（周鹏，上海师范大学）

Abstract: We first recall the well-known theory of two-species abstract competitive systems from the viewpoint of monotone dynamical systems.

Then focusing on the two technical conditions in the abstract theory, we report some recent development on how to realize these conditions in specific competition models,

especially in those infinite dimensional competition systems involving diffusion and even advection.