报告1

题目：Localized Big Bang Stability

报告人：郑纬航（Monash University）

时间：2026年6月9日(星期二)，9:00-10:00

地点：双清综合楼304

摘要：In the theory of general relativity, an important heuristic provided by Belinskii-Khalatnikov-Lifshitz (BKL) is that cosmological singularities should be either chaotic and oscillatory or quiescent. While the BKL conjecture has been studied for decades, the behaviour near such singularities remains incompletely understood. There is literature dating back to the last century suggesting some ideas about the Big Bang formation. For the quiescent case, the Kasner family of exact solutions to the Einstein-scalar field equations provides a key model, with solutions in the sub-critical regime exhibiting a quiescent Big Bang singularity characterized by blowing curvature invariants. Recently, a remarkable result was given by Fournodavlos-Rodnianski-Speck (FRS) where they proved the past nonlinear stability of the Kasner-scalar field solutions of the entire sub-critical regime. In this talk, I will discuss a stronger result of the FRS's work by establishing the localized stability, i.e. the stability on a truncated cone domain. This is joint work in part with Florian Beyer and Todd Oliynyk.

报告2

题目：Ultralocalization and AVTD Behaviour near the Big Bang

报告人：郑纬航（Monash University）

时间：2026年6月9日(星期二)，10:00—11:00

地点：双清综合楼304

摘要：In this talk, I will present an ongoing work based on the localized Big Bang stability. The BKL conjecture indicates spatial decoupling phenomenon near the cosmological singularities. The ultralocalization refers to the stability of the sub-critical Kasner-scalar field metrics on a complete cone domain. We show that near the Big Bang singularity, the perturbed solutions can be approximated by the flow map of a specific ODE system, which corresponds to the asymptotic velocity term dominated (AVTD) behaviour in the BKL conjecture. This is a joint work with Todd Oliynyk.

组织人：于品