I am interested in arithmetic combinatorics, combinatorial number theory, discrete Fourier analysis, geometric measure theory, and discrete geometry.
I defended my PhD thesis, titled Similar point configurations in vector spaces over finite fields and quotients of distance sets, on April 18, 2024, at the University of Rochester.
F. Rakhmonov, Distribution of similar configurations in subsets of F_q^d, Discrete Mathematics, (2023). [arXiv] [doi]
A. Iosevich, D. Koh, and F. Rakhmonov, The quotient set of the quadratic distance set over finite fields, Forum Mathematicum, (2024). [arXiv] [doi]
P. Bhowmik and F. Rakhmonov, Near optimal thresholds for existence of dilated configurations in F_q^d, Bulletin of the Australian Mathematical Society, (2024). [arXiv] [doi]
P. Bhowmik, A. Greenleaf, A. Iosevich, S. Mkrtchyan, and F. Rakhmonov, Similar point configurations via group actions, Illinois Journal of Mathematics, (2025). [arXiv] [doi]
J. M. Fraser and F. Rakhmonov, Exceptional projections in finite fields: Fourier analytic bounds and incidence geometry, Mathematische Zeitschrift, (2026). [arXiv] [doi]
J. M. Fraser and F. Rakhmonov, An improved L² restriction theorem in finite fields, Proceedings of the American Mathematical Society, (2026). [arXiv] [doi]
H. Kang, D. Koh, and F. Rakhmonov, The Erdős-Falconer distance problem between arbitrary sets and k-coordinatable sets in finite fields, Finite Fields and Their Applications, (2026). [arXiv] [doi]
J. M. Fraser and F. Rakhmonov, Lp averages of the discrete Fourier transform and applications, accepted for publication in Springer Proceedings in Mathematics & Statistics, "Combinatorial and Additive Number Theory VII", (2025). [arXiv]
Allan Greenleaf (1)
Alex Iosevich (2)
Pablo Bhowmik (2)
Jonathan Fraser (3)
Doowon Koh (2)
Sevak Mkrtchyan (1)
Hunseok Kang (1)
Kyle Yip (0)
Sophie Huczynska (0)