Home > News

Weinstein Hosts Workshop on Topologically Protected States

Apr 10 2017

Michael I. Weinstein, Professor of Applied Mathematics and Professor of Mathematics was lead organizer of the recent workshop on "Mathematical and Physical Aspects of Topologically Protected States” which took place at Columbia University from May 1-3, 2017. Co-organizers were Professor Shi Jin of University of Wisconsin and Professor Jianfeng Lu of Duke University.

The workshop was supported by Professor Weinstein’s Math + X Investigator Award from the Simons Foundation and by KI-Net, an National Science Foundation Research Network. The workshop, with about 60 participants, was aimed at the community of research mathematicians, physicists and engineers working in the very active field of “Topological Matter” and its analogues and applications in, for example, electronic physics, photonics and acoustics.
Workshop on  Mathematical and Physical Aspects of Topologically Protected States at Columbia University, May 1-3, 2017
Abstract: The field of Topological Insulators (TI) has its origins in phenomena in condensed matter physics such as the Quantum Hall Effect, followed by theoretical and experimental work on 2D crystalline materials, e.g. graphene, and more recently three-dimensional TIs. A hallmark of TIs is the existence of uni-directionally propagating states, localized within 1D line defects or 2D facets created from the bulk TI. Such states and their propagation properties are robust against spatially localized (even large) perturbations. With the recognition that many phenomena are related to the general properties of waves propagating in media with certain dispersion properties (e.g. periodic media with band structures having novel features such as symmetry-induced "Dirac points"), theoretical and applied physicists, and engineers have explored realizations of TI-like phenomena in, for example, photonics and acoustics. 
 
The mathematical and theoretical approaches taken to study TIs range from the analysis of PDEs and tight-binding models, to index theory, to non-commutative geometry, and computational aspects of these subjects. This workshop will focus on recent developments in this area at the interface of mathematics and fundamental and applied physics. The workshop is aimed at the broad group of researchers, with a view toward promoting interactions between the communities of mathematicians, physicists, and engineers. The organizers aim for the introductory part of each talk to be tutorial (at the first year graduate level) before focusing on more recent developments.

Goals: This workshop will focus on recent developments in this area at the interface of mathematics and fundamental and applied physics. The workshop is aimed at the broad group of researchers, with a view toward promoting interactions between the communities of mathematicians, physicists, and engineers. The organizers aim for the introductory part of each talk to be tutorial (at the first year graduate level) before focusing on more recent developments.

Organizers:  Shi Jin, University of Wisconsin-Madison: Jianfeng Lu, Duke University; and Michael I. Weinstein, Columbia University

 

Stay up-to-date with the Columbia Engineering newsletter

* indicates required