Mathematical and Physical Aspects of Topologically Protected StatesMay 1 - 3, 2017Columbia University |
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.
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.
REGISTRATION CLOSEDORGANIZERS |
CONFIRMED PARTICIPANTSFUNDINGA limited amount of funding for travel and lodging is available for researchers from Ki-Net nodes in the early stages of their career who want to attend the full program, especially for graduate students and post-doctoral fellows. INFORMATION FOR PARTICIPANTSDepartment of Applied Physics and Applied Mathematicsand Department of Mathematics Columbia University Email: miw2103@columbia.edu CONFERENCE POSTERACKNOWLEDGMENTFunding provided by Simons Foundation Math+X Investigator Award #376319, and the National Science Foundation through the Ki-Net Grant. |