NSERC Undergraduate Student Research Award project: Probing Exotic Fields. This project was conducted under the supervision of Professor Niayesh Afshordi. We were studying the possibility of using orbital quantum sensors to probe exotic scalar signals, such as (hypothetical) scalar radiations from binary black hole/neutron star mergers and the (hypothetical) cosmic scalar background predicted by some theoretical models. We have submitted our first paper on detecting cosmological scalar fields using orbital networks of quantum sensors to arXiv https://arxiv.org/abs/2311.17873. The second paper on probing scalar radiations from binary black hole/neutron star mergers is under construction.
IQC Undergraduate Research Award project: Approximately band-limited functions. This project was conducted under the supervision of Professor Eduardo Martin-Martinez. We were studying the sampling theory for non-band-limited functions and its applications, especially in superoscillations. Ultimately, we want to generalize the results in https://doi.org/10.1063/1.4996135 to the more realistic non-band-limited case and resolve some of the issues raised in this paper. We have also proposed a new way to characterize superoscillations, which is more general and robust than the widely used method. The manuscript is on arXiv https://arxiv.org/abs/2311.17703 and submitted to Journal of Physics A.
AMATH 875 final essay: Review of Spectral Geometry and its Applications to Quantum Gravity.
PHYS 437A final report: Sampling Theory for Approximately Band-limited Functions, Superoscillations, and the Preliminary Attempt to Characterize Non-band-limited Superoscillations.
PHYS 349 final project: a code that simulates gravitational lensing. Collaborated with Shen Zuo and Zhiyao Wang.
PMATH 863 final essay: an essay on the irreducible representations of the lie algebra sp_4 C. Collaborated with Jing Xuan Chen, Hanming Liu, Daniel Han and Xiao Zhong.
PHYS 442 bonus essay: Special Relativity and Group Representations.
PHYS 275 final essay: solar sail spacecraft.
AMATH 271 final project: research on the motion of the double pendulum system. [Link to the code] [Link to the animations]
AMATH 251 project: a project on the numerical methods of ODEs. [Link to the code]
An Introductory Theoretical Mechanics book for high school students. It was written in Chinese. Collaborated with Gaundi Zhao
Here are the courses that I will have taken by the end of the Winter 2023 term at the University of Waterloo:
Lecture notes are for learning purposes only. The copyright belongs to the authors. The lecture notes labelled “incomplete” will be updated once they are completed. The lecture notes labelled “not available” are either courses that do not have lecture notes or courses that have not been taken yet. They will be updated once they are available.
If you find any mistake in any of these notes, please contact me. I will correct them if possible.