Topological insulators(TIs) are materials characterized by topological invariants. One of their remarkable features is the asymmetric transport observed at the interface between materials in different topological phases. Such transport is itself described by a topological invariant, and therefore “protected” against random perturbations. This immunity makes TIs extremely promising for many engineering applications.

In this talk, we present a partial differential model for such TIs, introduce a topology based on indices of Fredholm operators, and analyze the influence of random perturbations on transport. We confirm that topology is an obstruction to Anderson localization, a hallmark of wave propagation in strongly heterogeneous media in the topologically trivial case. We quantify what is or is not protected topologically and show that, for instance, a quantized amount of transmission is protected while back-scattering, a practical nuisance, is not.

Guillaume Bal 教授目前任芝加哥大学数学系和统计系教授。他的研究领域是偏微分方程的应用分析，特别是反问题和含随机系数的偏微分方程。他是2011年的Calderón奖得主，并于2017年当选美国数学会Fellow。

Calderón 奖由国际反问题协会（IPIA)颁发，用来表彰在反问题领域作出杰出贡献的40岁以下的青年学者。该奖自2007年起，每两年颁发一次。