Large-scale geometry of topological phases

by Prof. Guo Chuan Thiang (BICMR, Peking University)

Thursday 3 Mar 2022, 16:30 → 17:30 Asia/Shanghai

S408

We know from experiments that topological phases exhibit spectral phenomena which survive significant geometric deformations and require no periodicity whatsoever. Thus the interesting perturbations explore regimes that go far beyond the idealized band theory. I will gently introduce coarse geometry and index theory as the mathematical core of the topological phase idea. As examples, we can rigorously analyse quantum Hall effects on strongly curved and dislocated 2D samples, and prove that anomalous gapless boundary states appear regardless of the small-scale specifics of the sample. Biography: Guo Chuan Thiang (程国传) joined the faculty of BICMR, Peking University, in 2021. Prior to this, he was an Australia Research Council DECRA Fellow at the University of Adelaide. He completed a DPhil in mathematics at the University of Oxford, a Master’s degree in mathematics at the University of Cambridge, and a Bachelor’s degree in physics and mathematics at the National University of Singapore. His research is in mathematical physics, particularly quantum theory and mathematical aspects of topological phases. Tencent Meeting: https://meeting.tencent.com/dm/CfYGZuuJIgZL Meeting ID：647-741-617