Spring 2018

Organizer : Dr. Yongki Lee and Dr. Yuanzhen Shao 

• Math Physics Seminar

  • Date: Thursday, April 12

  • Time: 2:30 – 3:30 PM 

  • Location: MP2028

  • Speaker: Dr. Shijun Zheng (Georgia Southern) 

  • Title:  Sharp Condition on Orbital Stability for Dispersive Models

  • Abstract: Vortex type solitons exhibit remarkable and ubiquitous phenomena in quantum optics, plasma, superfluids and pseudo-relativistic boson stars.

    • • I will start with an introduction on the soliton theory for NLSE and gKdV. Recent results on orbital stability and instability results will be reviewed. 

      • In the second part, I will address the threshold for global existence, blowup and stability for NLSE with rotation in 3D. 

      • As a governing equation for superfluids, such model gives rise to a hydrodynamical system in the semiclassical regime.   

      • The technical challenges come from the symmetry breaking between the rotational term and anisotropic trapping potential, where the angular momentum of

      • a particle is not conserved in time. This study is motivated by related open questions in the area in oder to understand the asymptotic behavior and rates of wave-collapse for the solutions.  It is worth mentioning that the stability results apply for other dispersive type equations including magnetic and fractional NLSE,  Klein-Gordon, Dirac, generalized Zakharov-Kuznetsov and some shallow water wave equations.

• Joint talk with Department Colloquium 

  • Date: Friday, April 13 

  • Time: 3:30 – 4:30 PM 

  • Location: Math/Physics Bldg 3314 

  • Speaker: Dr. Gong Chen (University of Toronto) 

  • Title: Strichartz estimates for linear Schroedinger and wave equations

  • Abstract: We will discuss Strichartz estimates which play a crucial role in the study of dispersive equations. This type of estimates can be regarded as dispersive version of Sobolev estimates. Starting from the connection to the famous Fourier restriction, I will discuss Strichartz estimates for free Schroedinger equation and wave equation. And then, I will try to explain how one can extend these estimates to perturbed linear equations which appear naturally in the study of stability of nonlinear structures and some applications.

• Joint talk with Applied Math and Computing research colloquium 

  • Date: Thursday, April 19 

  • Time: 3:30 – 4:30 PM 

  • Location: MP 1316

  • Speaker: Dr. Ionut Emil Iacob (Georgia Southern) 

  • Title: Machine Learning: concepts, methods, and some applications

  • Abstract: Machine learning consists of techniques for learning from and making prediction about data. We will begin by explaining supervised and unsupervised learning concepts and surveying some of the most popular methods for performing these tasks. We will then focus on Support Vector Machines and Artificial Neural Networks and discuss some of their applications. This will be an introductory talk, aimed at a broad audience.

• Joint talk with Department Colloquium 

  • Date: Friday, April 27

  • Time: 3:30 – 4:30 PM 

  • Location: Math/Physics Bldg 3314 

  • Speaker: Dr. Marcelo Disconzi (Vanderbilt University) 

  • Title: Recent developments in the theory of relativistic fluids

  • Abstract: We will discuss some recent results concerning mathematical aspects of relativistic fluids, focusing on the evolution problem for Einstein’s equations coupled to the equations of relativistic fluid dynamics. After introducing some background, we will present two alternative formulations of the relativistic Euler equations. The first one is inspired on work by H. Friedrich and employs a frame formalism to recast the Einstein-Euler system as a first order symmetric hyperbolic system. We will give a motivation behind this approach and establish an existence and uniqueness result. The second formulation reveals a remarkable null-structure of the relativistic Euler equations. Such structure is “hidden,” i.e., it is not apparent in the equation’s usual form, and has important consequences for the study of the nature of shock formation. We will then turn our attention to the problem of relativistic fluids with viscosity. The question of how to formulate viscous fluids within relativity theory goes back to Eckart in 1940 and remains largely open. After discussing the history of the problem and reasons for considering relativistic viscous fluids, we will present a recent formulation that provides the first example in the literature of a theory of relativistic fluids with viscosity that admits existence and uniqueness of solutions when coupled to Einstein’s equations, and satisfies further requirements intrinsic to relativistic theories. Some of the results I will discuss are joint with F. Bemfica, M. Czubak, J. Noronha, and J. Speck.