Seminar 15, Wednesday 28 October 2020, 14:00 (London Time)
Speaker : Michael I Weinstein (Dept of Applied Physics and Applied Mathematics, and Dept of Mathematics, Columbia University)
Title: Dynamics of waves in continuum honeycomb structures
Abstract: We overview results on the dynamics of waves (e.g. Schroedinger and Maxwell equations) in honeycomb structures and their deformations.
We study phenomena which arise from the presence of Dirac (conical) points in the bulk band structure.
These include the existence of robust edge (interface) states, which localize along certain sharp terminations, and along domain walls.
We then discuss recent work on the emergence of pseudo-magnetic fields in non-uniformly deformed honeycomb structures.
We apply these results to predict Landau-like energy levels in photonic crystals, and present numerical confirmation of the theory.
Biography: Michael I. Weinstein works on the mathematical modeling, analysis, and applications of wave phenomena across many areas of physical science. A recent focus has been on PDE (Partial Differential Equations) models which describe optical and quantum waves in novel media such as topological insulators and metamaterials. Such physical media have applications to technologies which could potentially revolutionize robust information transfer in computing and communication systems. Weinstein received a B.S. in Mathematics from Union College, summa cum laude, in 1977 and a Ph.D. in Mathematics from the Courant Institute at NYU in 1982. He is a Professor of Applied Mathematics in the Department of Applied Physics and Applied Mathematics and a Professor of Mathematics in the Department of Mathematics at Columbia University. Weinstein is a Fellow of the American Mathematical Society (AMS) and a Fellow of the Society for Industrial and Applied Mathematics (SIAM). In 2015, he received a Math + X Investigator Award from the Simons Foundation.