Title1: Blow-up Energy Thresholds for the Hartree Equation with a Focusing Subcritical Perturbation

Speaker:   Prof. Shihui Zhu  ( Sichuan Normal University )

Time: Wed, Apr.21 2021, PM: 15:00-16:00

Location: Tencent Conference

Meeting  Number: 778 556 134

Title2: Asymptotics of the Pearcey determinant

Speaker:   Prof. Lun Zhang  ( Fudan University )

Time: Wed, Apr.21 2021, PM: 16:00-17:00

Location: Tencent Conference

Meeting  Number: 778 556 134

Inviter: Prof. Liming Lin

Abstract:

           This paper assesses the blow-up solutions for the Schrödinger equation with a Hartree-type nonlinearity together with a power-type subcritical perturbation. The precisely sharp energy thresholds for blow-up and global existence are obtained by analyzing potentially valid structures for associated functionals. This work joint with Tian Shuai, Yang Ying, Zhou Rui.

Abstract:

        The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a variety of statistical physics models beyond matrix models as well. In this talk, we are concerned with the Fredholm determinant , where  and  stands for the trace class operator acting on  with the Pearcey kernel. We obtain asymptotics of this determinant as , which is also interpreted as large gap asymptotics in the context of random matrix theory. It comes out that the Pearcey determinant exhibits a significantly different asymptotic behavior for and, which suggests a transition will occur as the parameter  varies. This talk is based on two recent joint works with Dan Dai and Shuai-Xia Xu.