Symbol of String
| Date | Speaker | Title and Abstract |
| Friday April 7th, 3:30--4:30 PM (Joint with Colloquium) |
Chen-Jie Fan (MIT) | "On Focusing Mass Critical NLS at The Regularity of L^2" We will explore the dynamic of non-scattering L^2 solution u to the radial mass critical nonlinear Schroedinger equation with mass just above the ground state, and show that there exists a time sequence {t_n}_n, such that u(t_n) weakly converges to the ground state Q up to scaling and phase transformation. |
| Friday April 14th, 3:30--4:30 PM (Joint with Math-Physics Seminar) |
Tuoc Van Phan (University of Tennessee, Knoxville) | "Asymptotic stability of solitary waves in 1D nonlinear Dirac Equations" In this talk, I will discuss about my joint work with Andrew Comech (TX A&M) Atanas Stefanov (Kansas U) on nonlinear Dirac equation in 1D with scalar self-interaction (Gross–Neveu model), with quintic and higher order nonlinearities (and within certain range of the parameters). We show that solitary wave solutions are asymptotically stable in the “even” subspace of perturbations. The asymptotic stability is proved for initial data in H1-space. The approach is based on the spectral information about the linearization at solitary waves which we justify by numerical simulations. For the proof, we develop the spectral theory for the linearized operators and obtain appropriate estimates in mixed Lebesgue spaces, with and without weights. |
| Friday November 4th, 3:30--4:30 PM (Joint with Colloquium) |
Sohrab Shahshahani (University of Michigan) |
"Wave Maps on Hyperbolic Spaces" Abstract: The wave map equation is a generalization of the usual linear wave equation to functions which take values in a Riemannian manifold. Unlike the linear wave equation, the geometry of the wave map problem makes the equation nonlinear. The equation is the hyperbolic analogue of the elliptic harmonic map equation and the parabolic harmonic map heat flow from Riemannian geometry. In this talk I will review some of the important developments in the study of wave maps over the past couple of decades, most of which concern wave maps from a flat domain. I will then describe new phenomena which arise from considering curved backgrounds. I will focus on wave maps from hyperbolic spaces, discussing joint works with Andrew Lawrie and Sung-Jin Oh. |
| Wednesday September 7th, 1:25-2:15 PM (Joint with Math-Physics Seminar) |
Shijun Zheng (GSU) |
"Minimal mass-energy dynamics for Solitons arising in Mathematical Physics" Abstract: It has been over decades for the study of dispersive evolutionary models ranging from water waves to quantum particles and gases, where is applied the theory of Bose-Einstein statistics, Femi-Dirac statistics or Maxwell-Boltzmann statistics. However the mathematical understanding of large time asymptotic behaviors of those nonlinear waves are rather poor. We present an overview of recent progress on the rigorous description of such behaviors in term of long time existence and blowup, regularity as well as the solitary waves. This reveals an integral portion of the grand conjecture, the so-called Soliton Resolution Conjecture. In particular, numerical results are presented for the excited states for Gross-Pitaevskii equation (NLSE) with rotation. The initial data is taken to be the ground state, Gaussian or Thomas-Femi 2 in the observation. |
Symbol of String