数学研究所
学术报告
调和分析和偏微分研讨班
Speaker: Prof. Lars Andersson （BIMSA）
Title: Stability of spacetimes with supersymmetric compactifications.
Time&Venue: 2024年12月20日（星期五） 15:00-16:00 & S813
Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and Shing-Tung Yau.
Speaker: 张笑然（BIMSA）
Title: A review of Soffer-Weinstein's proof of instability in Hamiltonian, resonant nonlinear wave equations
Time&Venue: 2024年12月20日（星期五） 16:00-17:00 & S813
Abstract: We will give a review of Soffer, Weinstein's work[Invent. math. 1999]. They consider a class of nonlinear Klein-Gordon equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. They showed that, for generic nonlinear Hamiltonian perturbations, all small amplitude solutions decay to zero as time tends to infinity at an anomalously slow rate, because of the resonance. In particular, spatially localized and time-periodic solutions of the linear problem are destroyed by generic nonlinear Hamiltonian perturbations via slow radiation of energy to infinity.
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