Research

Over the last ten years, I have pursued a broad range of research topics. My main research interests are: discrete harmonic analysis, analytic number theory, and moments of arithmetic functions. I have completed research projects in ergodic theorem, primes distribution, partitions theory, and additive number theory. In the past, I have published research papers in algebraic coding theory, cryptography, and wireless sensor networks. Here is my Google scholar profile.





Publications

You can also check the most updated version of my papers in my Google scholar profile.

1. "On a Class of Sums With Unexpectedly High Cancellation, and Its Applications", with E, Croot. Submitted. 2021. arxiv link

2. "Endpoint l^r Improving Estimates for Prime Averages", Math Research Letters, with Michael Lacey and Y. Rahimi. 2021 arxiv link

3. "Factorization Theorems for Relatively Prime Divisor Sums, GCD Sums and Generalized Ramanujan Sums", The Ramanujan Journal, with M. Schmidt. 2021 arxiv link

4. "On Reduced Archimedean Skew Power Series Rings", Journal of Algebra and Its Applications, With A. Qureshi and F. Padashnik. 2020 arxiv link

5. "On Skew Cyclic Codes Over a Finite Ring", Iranian Journal of Mathematical Science and Informatic, with R. Mohammadi, S. Rahimi. 2019 here

6. "Characterization of the Skew Cyclic Codes Over Fp + uFp". International Journal of Information and Coding Theory, with R, Dastbasteh, T. Abualrub, J. Haghighat, N. Aydin. 2018 here

7. "Skew Cyclic Codes Over Fp +vFp +v2Fp". Bulletin of Korean Mathematics, with A. Moussavi, S. Rahimi. 2018 here

8. "A New Approach to Decrease the Computational Complexity of E-voting Protocols", Transactions on Emerging Telecommunications Technologies, with B. Ahmadi, S. Rahimi. 2017. here

9. "The Hardy-Ramanujan-Rademacher Expansion for the Partition Function And its Extensions", Master dissertation at Sabanci University. 2017. here

10. "Analysis of a Subset Selection Scheme for Wireless Sensor Networks in Time-Varying Fading Channels", IEEE Transaction on Signal Processing, with J. Haghighat, W. Hamuda, R. DastBaste. 2016. here

11. "A Relay Subset Selection Scheme for Wireless Sensor Networks Based on Channel State Information", IEEE International Conference on Communications (ICC, Malysia), with J. Haghighat, W. Hamuda. 2016 here

12. "A Relay Subset Selection Scheme for Wireless Sensor Networks for Almost Quasi-static channels", second Iranian Conference on Communications Engineering (ICCE Iran), with J. Haghighat, M. Eslami. 2016

13. "Study the logical philosophical conformity of Iranian traditional medicine and their treatments", 14th Iranian Pharmaceutical Sciences Congress (Iran), with M. Farahmandnejad, P. Salehi Nowbandegani, P. Faridi. 2015.

Preprints & Works in Progress

1. "Improving and Maximal Inequalities for Primes in Progression", With M, Lacey, Y, Rahimi, and C, Giannitsi.

2. "Improving Inequalities for Gaussian Primes", with M, Lacey.

3. "On a problem of Graham, Erdos, and Pomerance on the p-divisibility of Central Binomial Coefficients", with Ernie Croot.

4. "l^p-boundedness of the Carleson Operators", with B.Krause and M. Lacey.

5. "An Exact Formula for the Number of Partitions With Parts of the Form pt + a", with K.Kursungoz.

6. "On the Structure of Primary Ideals of a Non-Laskerian Group Ring", With R, Dastbasteh.



Talks

1. "Recent Progress on Vinogoradov Mean Value Theorem", Oral Comprehensive Exam , Georgia Tech, USA. 2021.

2. "Chain Conditions over Power Series and Polynomial Rings", Algebraic Geometric Student Seminar, Georgia Tech (Virtual), USA. 2021. Slides Abstract

3. "Sums with High Cancellation and the Distribution of Primes", Analysis Student Seminar, Georgia Tech, USA. 2021. Abstract

4. "A Class of Sums With Unexpectedly High Cancellations", Combinatorial and Additive Number Theory (CANT), CUNY Graduate Center (Virtual), USA. 2020. Slides Abstract

5. "On a Class of Sums with Unexpectedly high Cancellation and PTE Problems", ACO Seminar, Georgia Tech, USA. 2019. Slides Abstract

6. "Pentagonal Number Theorem and Zeroes of Riemann Zeta Function", The Legacy of Ramanujan and in honor of Bruce Berndt's 80th birthday, University of Illinois at Urbana Champaign, USA. 2019. Slides Abstract

7. "A Homomorphic E-Voting Protocol Based on El-Gamel Cryptosystem", Women in STEM Conference, Georgia State University, USA. 2019. Slides Abstract

8. "Three circle Theorem and Moments of Riemann Zeta Functions", Georgia Tech, US. April 2019. Slides

9. "Number of Partitions with Parts of the Form pt + a", Integers Conference, USA. October 2018. Slides Abstract

10. "What is Weil Conjecture?", Georgia Tech. US. 2017. Slides

11. "Skew Cyclic Codes", Algebraic Coding Theory Workshop, Sabanci University. Turkey. May 2017.

12. "The Hardy-Ramanujan-Rademacher Expansion for the Partition Function And its Extensions", Master's defense, Sabanci University, Turkey, 2017. Slides Abstract

13. "Wireless Sensor Networks in Correlated Fading Channels", Three-minute Thesis Competition, Modarres University. 2016.

14. "Homomorphic E-Voting Protocols", Cryptology Seminars, Beheshti University, Iran. 2016.

15. "Performance Study of Wireless Sensor Networks in Correlated Fading Channels", Master's defense, Shiraz Tech, Iran. 2015. Slides Abstract

16. "A Few Famous Conjectures on the Density of Prime Numbers in Higher Degree Polynomials", Shiraz university. Iran. June 2013.

17. "Topology of Numbers", Week of Mathematics, Iran. Shiraz university. Iran. 2011.

Workshop Participation

Collaborated on research talk in a conference in honor of George Andrew's 80th birthday, Penn State university, USA. 2018. Link of Conference

Spring School on Analytic Number Theory, IPM, Iran. 2016. Link of School

Participated in Iranian Workshop on Communication and Information Theory(IWCIT), Tehran. Iran, 2014. Link of Workshop

Selected Awards

Research Assistant supported by NSF Grant (M, Lacey. DMS-1949206), Georgia Tech, USA, Fall 2021.

Research prize supported by NSF Grant (M, Lacey), $1500, Georgia Tech, USA, 2020.

Top three Researcher Students (Gursel Award), $800, Sabanci University, Turkey, 2017. About the Award

Awarded NEFI (National Elite Foundation of Iran) gifted prize, $4000, Iran, 2014- 2015. About the Award

Gold medal in 36th Iranian Mathematics competition for university students, Iranian Math Society, 2012.

Silver Medal in 17th Regional Mathematic Olympiad for university students, Iranian Math society, 2013.