Time：16:00-17:00, Friday, Nov 11, 2022
ZOOM ID:863 6606 6486
PASSCODE:738489
Host:Dr. Xing Gu, Institute for Theoretical Sciences, Westlake University
Speaker：Dr. Yifei Zhu,an assistant professor at the Department of Mathematics of the Southern University of Science and Technology. His research interests are in algebraic topology and related fields, particularly in its connections to algebraic geometry and number theory via objects such as formal groups, elliptic curves, and modular forms.
Title：Topology of stratified singular moduli spaces for gapless quantum mechanical systems
Abstract：
This talk presents an external application of the algebraic topology of moduli spaces. In condensed matter physics, the Hamiltonian of a quantum mechanical system takes a mathematical form of a square matrix, with parameters functions on the 3D momentum space. Such a matrix satisfies the Hermitian symmetry, so that its eigenvalues are real and represent observed energies. We will discuss this space of parameters for Hamiltonians, especially its degeneracy locus where eigenvalues occur with multiplicities. Such a locus gives rise to exceptional properties in the larger scale, with applications to the design of sensing and absorbing devices. We focus on certain non-Hermitian Hamiltonians, the imaginary parts of whose eigenvalues model energy exchange of open systems. Their parameter space possesses intriguing topology, with a stratification of non-isolated singularities, which affords interesting phenomena such as the so-called bulk–edge correspondence. The associated algebraic invariants enable classifications and predictions for phases of matter. This work is in collaboration with C. T. Chan, Jing Hu, Hongwei Jia, Xiaoping Ouyang, Yixiao Wang, Yixin Xiao, Ruo-Yang Zhang, and Zhao-Qing Zhang.
