I am interested in Fourier analysis and related problems in Geometric measure theory. One of the most important questions in Geometric measure theory is: How large does a given set in vector space ( R^d) need to be to make sure that it contains copies of a given configuration of points?
For example, I am interested in Falconer distance conjecture and related problems.
On Hausdorff dimensions of k-point configuration sets via Fourier integral operators, in preparation.
On the Falconer type functions and the distance set problem, arXiv:2510.15118, submitted.
Lp -integrability of functions with Fourier supports on fractal sets on the moment curve, with S. Duan and D. Ryou, J. Funct. Anal. 289 (2025), no. 12.
Packing sets in Euclidean space by affine transformations, with A. Iosevich, P. Mattila, E. Palsson, T. Pham, S. Senger, and C-Y. Shen (2024), arXiv:2405.03087, submitted.
Pinned simplices and connections to product of sets on paraboloids, with A. Iosevich, T. Pham, and C-Y. Shen, Indiana Univ. Math. J. 74 (2025), no.3, 647-668.
Discretized sum-product type problems: Energy variants and Applications, with T. Pham, and C-Y. Shen (2022), submitted.
Structural theorems on the distance sets over finite fields, with D. Koh and T. Pham, Forum Math. 35 (2023), no.4, 925-938.
On the k-resultant modulus set problem on varieties over finite fields, Int. J. Number Theory 19 (2023), no.3, 569-579.
Bound for volumes of sub-level sets of polynomials and applications to singular integrals, with Loi Ta Le (2020).