Greetings. I am a PhD student at the University of British Columbia (UBC) working with Malabika Pramanik and Joshua Zahl. I am interested in Harmonic Analysis.
Prior to coming to UBC, I did my master's degree at Peking University (PKU) with Baoping Liu. Before that, I was an undergraduate of Beijing University of Posts and Telecommunications (BUPT).
I can be reached via wangcaiji5054@gmail.com or Room 4131, Earth Sciences Building (ESB).
I am interested in Euclidean Fourier Analysis involving curvature as well as its related problems/tools from Geometric Measure Theory and Incidence Geometry.
The notes and slides* I wrote are the following.
Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions after H. Wang and J. Zahl*, with Sam Craig, Peiqi Nie, Yixuan Pang. Full slides*.
A note on a pinned variant of Bourgain's theorem for $k$-point patterns in $\mathbb R^d$.
Kakeya conjecture over $\mathbb Z/ N\mathbb Z$ after M. Dhar, with Xu Zheng.
A Roth-type theorem for dense subset of $\mathbb R^d$ after B. Cook, A. Magyar and M. Pramanik, with Angel Cruz. Slides*.
Harmonic analysis seminar at UBC
High/low method in harmonic analysis (Fall 2025)
Wednesday 16:00 - 18:00, ESB 4127
Notes (updated on 2025.08.30)
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At UBC, besides answering general questions at the Math Learning Centre (MLC), my teaching assistantship duties include providing feedback on homework submissions, tutoring students online, creating engaging problems to meet desired learning outcomes, and grading for the midterm/final exams.
As a teaching assistant, I supported the following courses.
2025 Term Fall: MATH 215: Elementary Differential Equations I
2024 Terms Spring/Fall: MATH 215: Elementary Differential Equations I, MATH 253: Multivariable Calculus
2023 Terms Spring/Fall: MATH 227: Advanced Calculus, MATH 120: Honors Differential Calculus