Nabla Seminar

Grad Analysis Seminar at Rutgers University

Grad Analysis (\nabla) Seminar is a graduate seminar at Rutgers University, Department of Mathematics, Orgnized by Qi Ma since Nov. 2024.

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Here is the latest information for our seminar:

2026 Apr.20th , Speaker: Kangbai Yan

Title: Singular Initial Value Problems for Wave Equations with Applications to Black Holes

Abstract: This talk concerns the singular initial value problem for a model nonlinear wave equation near a spacelike singularity. I will begin by briefly recalling the standard local existence theory and breakdown criteria for wave equations with regular initial data, together with Fritz John’s classical finite-time blow-up result. Motivated by explicit singular solutions of the Einstein vacuum equations, such as Kasner and Schwarzschild spacetimes, I will then discuss the model equation $\[ \Box_g \phi = (\partial_t \phi)^2 \]$ on a singular background metric (g). The central question is whether one can prescribe asymptotic behavior at the singular time and construct solutions evolving away from it. I will explain the construction of approximate solutions and the accompanying energy estimates for the remainder. Time permitting, I will also comment on the relation of this problem to the study of black hole interiors, in particular to questions surrounding strong cosmic censorship.

To see more detailed information of our seminar, please come to the pages below:

• 2026 Spring

• 2025 Fall

• 2025 Spring

• 2024 Fall