Spring 2024

Joint talk with Department Colloquium 

• Date: Friday, February 9

• Time: 4-5 PM 

• Location: ZOOM

• Speaker: Dr. Eric Stachura (Kennesaw State University)

• Title: Mathematical Methods in Liquid Crystal Optics

• Abstract: Liquid crystals are like non-Newtonian fluids. One of the most important features of the material are its optical properties, which are also responsible for the most common applications to displays. From an optical point of view, the material behaves more like a solid crystal. In general, liquid crystals are optically inhomogeneous and anisotropic, which presents unique challenges in geometric optics since this means the refractive index depends both on position and direction (compare to classical isotropic materials where the refractive index, which in some sense describes how fast light propagates in a medium, is a constant). In this talk, I will discuss some mathematical background to study optical problems (such as lens design) in liquid crystals. We will see that tools from the calculus of variations, Riemannian geometry, and partial differential equations come into play. Finally, I will discuss a sample variational problem as well as a list of open directions.

Joint talk with Department Colloquium 

• Date:  Friday, March 29

• Time: 3:30-4:30 PM 

• Location: Math/Physics Bldg, Room 3001

• Speaker: Dr. Xiaoxu Wu (The Fields Institute)

• Title: The Three-Quasi-Particle Scattering Problem

• Abstract: A quasiparticle is a concept in condensed matter physics and quantum mechanics that represents the collective behavior of particles within a material, such as electrons in a solid, mimicking the properties of individual particles. In this talk, I will focus on the scattering theory for three-quasiparticle systems. Quantum scattering theory's primary objective is to classify the potential long-time behaviors of solutions to quantum systems, a concept known as asymptotic completeness (AC). During this talk, I will present a new approach to proving AC, which is based on recent collaborative research with Avy Soffer.

• Short Bio: Dr. Xiaoxu Wu is currently a visiting member at the Fields Institute. She obtained her Ph.D. from Rutgers University in 2023. Her particular interests include the scattering theory, quantum information, and wave turbulence theory.