Spring 2025

• Math Physics Seminar

  • Date: Thursday, March  13 

  • Time: 3:30-4:30 PM 

  • Location:  Math/Physics Building  Room 3314

  • Speaker: Dr. Yi Hu (Georgia Southern University)

  • Title: Damped nonlinear Schrödinger equation with Stark effect

  • Abstract: In this talk, we will introduce the nonlinear Schrödinger equation with a Stark potential and a linear damping. In particular, we study the solution in the mass-critical case, and we will characterize the threshold for global existence and finite time blow-up. We will also present the log-log blow-up speed that the solution flow admits for certain initial data above the ground state.

• Joint talk with Department Colloquium 

  • Date: Friday, April 11

  • Time: 3:30-4:30 PM 

  • Location: Math/Physics Building  Room 3314

  • Speaker: Dr. Maja Tasković  (Emory University) 

  • Title: Kinetic theory equations and their associated hierarchies

  • Abstract: In statistical mechanics, a large number of interacting objects is modeled by considering the average behavior of the ensemble rather than that of individual objects. The resulting effective equations are called kinetic equations. In this talk we will focus on the wave kinetic equation which models (weakly nonlinear) interacting waves and we will address its global in time well-posedness by applying techniques inspired by the analysis of the Boltzmann equation, which is another kinetic equation that models rarefied gases in which interactions happen between particles.

We will also discuss the well-posedness of the wave kinetic hierarchy, which is an infinite system of coupled equations closely related to the wave kinetic equation, and the analogous result for the Boltzmann hierarchy. Two essential tools for obtaining these results are the Hewitt-Savage theorem, which allows us to lift the existence result for the equation to the hierarchy, and the Klainerman-Machedon board game argument, which allows us to control the factorial growth of the Dyson series and consequently prove uniqueness of solutions.

• Math Physics Seminar

  • Date: Thursday, April  17 

  • Time: 3:30-4:30 PM 

  • Location:  Math/Physics Building  Room 3314

  • Speaker : Mr. Jeffrey Heward (Georgia Southern University)

  • Title: Variational simulation of atom interferometry sequences in the presence of anharmonic potentials

  • Abstract: We have studied 1D and 3D atom interferometry (AI) sequences carried out with Bose-Einstein condensates (BECs) in the presence of external potentials consisting of harmonic plus anharmonic terms. The process where a BEC is split into multiple clouds and then recombined to form an interference pattern was numerically simulated by solving the Gross-Pitaevskii equation (GPE). Approximate solutions to this equation were generated using the Lagrangian Variational Method (LVM) whose trial wave function consisted of a sum of Gaussian functions, one for each cloud.  We derive the LVM equations of motion as well as a formula for the phase of the trial wave function. The variational result is compared to the numerical solution of the GPE. We will also compare these results with those given by time-dependent perturbation theory.

• Math Physics Seminar

  • Date: Friday, April  25 

  • Time: 2:30-3:30 PM 

  • Location:  Math/Physics Building  Room TBA

  • Speaker: Dr. Shijun Zheng (Georgia Southern University)

  • Title: Higher order Hamiltonians

  • Abstract:  The higher order dispersion phenomenon arises in propagation of  intense laser beams in the Kerr medium and magnetic materials. In the study of stability of solitons, one is led to the consideration of global in time existence of the solution of a fourth-order NLS system. Such systems can be derived from the Lagrangian and Hamiltonian formulations. I shall illustrate the physical implications by initially looking at examples involving the simple classical and quantum harmonic oscillators.