My research interests are in analysis. More specifically, I am interested in problems in geometric measure theory of Euclidean spaces. These problems fascinate me because they interconnect different parts of mathematics, such as:
Harmonic analysis
Fractal geometry
Additive combinatorics
Descriptive set theory (with its application to combinatorial problems in geometric measure theory)
Polynomial methods and finite-field analogues.
Before I pursued mathematics, I was a theoretical physicist in training. Hence, I also have some interest in mathematical physics and mathematical problems arising in theoretical physics.
(with Chun-Kit Lai) Interior of certain sums and continuous images of very thin Cantor sets (submitted) arXiv:2410.01267 [math.MG][math.CA][math.DS]
(with Chun-Kit Lai) Topological Erdős similarity conjecture and strong measure zero sets (submitted) arXiv:2410.01275 [math.CA][math.LO][math.MG]
(with Krystal Taylor) Interior of distance trees over thin Cantor sets (submitted) arXiv:2507.07385 [math.CA]
(with Chun-Kit Lai & Yuveshen Mooroogen) Fifty years of Erdős similarity conjecture, Res Math Sci 12, 9 (2025) [Journal] [arXiv:2412.11062 [math.CA][math.MG]]
Interweaving Algebraic and Geometric Viewpoints in Quantum Field Theories (Fulfillment for Qualifying Exam as a Physics Ph.D Candidate. I also have presentation slides.)
Chiral Algebras in Two and Four Dimensions (Lecture note for my Junior Research Talk at APCTP.)
Liouville Integrability (Project in the Course PH 505 Classical Mechanics)
Holographic Renormalization: Massive Scalar on AdS (Project in the Course PH 654 Relativistic Quantum Field Theory II)
Orientation and thickness dependence of magnetic levitation force and trapped magnetic field of single grain YBa2Cu3O7-y bulk superconductors (Published in Progress in Superconductivity and Cryogenics)
Eilenberg-MacLane Spaces (Project in the Course MATH 850 Algebraic Topology)
Banach Algebras (Project in the Course MATH 711 Functional Analysis)
Hausdorff Measure and Hausdorff Dimension (Project in the Course MATH 710 Measure and Integration)