Research

Papers

Averages with the Gaussian divisor: Weighted Inequalities and the Pointwise Ergodic Theorem with Nazar Miheisi, and Hamed Mousavi. arXiv
Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates, with Ben Krause, Michael T. Lacey, Hamed Mousavi, and Yaghoub Rahimi. (submitted) arXiv
A lower estimate on the square function of an indicator set, with Michael T. Lacey.
Proceedings of the AMS (early access). doi, arXiv
Improving and Maximal Inequalities for Primes in Progressions, with Michael T. Lacey, Hamed Mousavi, and Yaghoub Rahimi.
Banach J. Math. Anal. 16, 42 (2022). doi, arXiv
Averaging with the divisor function: ℓp improving and sparse bounds.
Rocky Mountain J. Math. 52(6): 2027-2039 (2022). doi, arXiv

Thesis: "Improving and Maximal Inequalities in Discrete Harmonic Analysis" (pdf)
Proceedings of the summer school "Discrete Analysis and Complexity of Quantum Algorithms" (pdf)
Master's thesis: The Reflection Principle on the Hyperbolic Plane (pdf in Greek)

Thesis: "Improving and Maximal Inequalities in Discrete Harmonic Analysis" (slides)
Presentation "Gaussian Primes: Improving Estimates and Goldbach's Conjecture" (slides)
Presentation "A lower estimate on square functions of indicators" (slides)
Presentation "Improving and Maximal Inequalities for Primes in Progressions" (slides)
Presentation "A brief introduction to the circle method and sparse domination" (slides)
Presentation "Averaging with the divisor function: ℓp improving and sparse bounds." (slides)