Fall 2021 - present: Ph.D. Thesis Research at the University of Waterloo. Supervisors- Dr. Yu-Ru Liu and Dr. Wentang Kuo. Working Project Title- On the distributions of divisor counting functions. This project aims to study the distribution of the omega-function and its refinements over natural numbers, and certain subsets of natural numbers. We explore various properties of the omega-function, such as the normal order and the Erdős-Kac Theorem. We extend this study to include all abelian monoids. The work done in this project will constitute to form my Ph.D. thesis which I plan to defend in Winter 2025.
 

Summer 2024: PIMS/BIRS Team Up! Pathways to Inclusive Research program at the Banff International Research Station, Banff, Calgary. Co-researchers- Habiba Kadiri and Allysa Lumley. Project Title- Generalizations of the Prime Number Theorem. This project aimed to investigate Bessel-type integral functions that arise in the study of prime number theorems and their generalizations and provide sharper explicit upper and lower bounds to these functions. We are in the process of completing a paper based on this research.
 

Summer 2023 & Summer 2024: Research Trips to Lethbridge hosted at the University of Lethbridge, Alberta. Co-researchers: Habiba Kadiri and Nathan Ng. Project Title- An explicit version of Chebotarev's density theorem. With these two research trips, we moved forward towards completing the project which is a continuation of my master's research. We are planning to submit an article based on this research soon.
 

Summer 2023: Team-up project at the Banff International Research Station, University of British Columbia, Okanagan campus. Co-authors: Swati Gaba, Ethan Lee, Aditi Savalia, and Peng-Jie Wong. Project Title- Explicit zero-free regions for Dedekind zeta functions. This project aimed to improve the zero-free region for the Dedekind zeta function. This involved studying earlier research on this topic and using new techniques available including the Deuring-Heilbronn phenomenon and the integral representation of the gamma function. We are in the process of completing the paper based on this research.
 

Winter 2021 - Spring 2021: Research Associate at the University of Lethbridge. Supervisors: Dr. Habiba Kadiri and Dr. Nathan Ng. Project Title- An explicit version of Chebotarev's density theorem - II}. This project aimed to provide explicit bounds for the error terms involved in Chebotarev's density theorem for the lower range of x, i.e. range of the form x < C for some constant C. My master's research studied the case x > C and this new research was carried out to complete the study of providing explicit bounds for Chebotarev's density theorem in the unrestricted range of all positive real numbers. Due to our recent project on studying the Bessel-type integral functions which are involved in the study of Chebotarev's density theorem, we have all the tools required to complete this research and submit an article based on this soon.
 

Fall 2018 - Fall 2020: Research Assistant and Master's Thesis at the University of Lethbridge. Supervisors: Dr. Habiba Kadiri and Dr. Nathan Ng, Project Title- An explicit version of Chebotarev's density theorem. This project aimed to prove a completely explicit version of Chebotarev's density theorem. An effective version of this theorem was proved by Lagarias and Odlyzko in 1975 and an explicit version was proved by Winckler in 2018. I improved Winckler's results by studying new techniques and ideas from articles by Faber and Kadiri, Kadiri and Lumley, Fiorilli and Martin, Bennett et al., and Hasanalizade et al. and generalized them to number fields. I used explicit results concerning the zeros of Dedekind zeta-function from articles by Trudgian, Lee,  Kadiri, and Ng, Hasanalizade et al., and Ahn and Kwon. The work done in this project formed part of my master's thesis which I defended on Dec 18, 2020. We are currently writing an article based on this research.
 

Fall 2016 - Spring 2018: Semester Projects at NISER, Bhubaneswar. Supervisor- Dr. Jaban Meher.

    - 9th and 10th Semester Project (Final year), Project Title- Solving Diophantine equations using elliptic curves. This was my Integrated Master's thesis whose aim was to study elliptic curves and modular forms and understand their application in the form of modularity theorem, level lowering theorem, and Frey curves to solve Diophantine equations, such as Fermat's last theorem and equations of the form a^p + 2^r  b^p  + c^p = 0, where p >= 5, a b c != 0 and a,b,c are pairwise co-prime except when r=1 and (a,b,c) = \pm (-1,1,-1).

    - 8th Semester Project, Project Title- Congruent Numbers and Elliptic Curves. The project aimed to study books like "Introduction to Elliptic Curves and Modular Forms (Chapters 1 and 3)" by N Koblitz and papers like "Congruent Numbers and Elliptic Curves" by J Brown and "The Congruent Number Problem" by V Chandrasekhar.
   
    - 7th Semester Project, Project Title- Rational Points on Elliptic Curves. The project aimed to learn the properties of rational points on an elliptic curve by studying "Rational Points on Elliptic Curves (Chapters 1,2 and 4)" by Joseph H. Silverman and John Tate.

    

Summer 2014 - Summer 2017: Summer Internships in India. These projects were funded by the Innovation in Science Pursuit for Inspired Research (INSPIRE) scholarship granted by the Ministry of Human Resource Development (MHRD).

    - Summer 2017, IISER, Bhopal. Supervisor- Dr. Karam Deo Shankhadhar. Project Title- An introduction to p-adic Numbers. This project aimed to analyze the properties of p-adic numbers by studying the book "p-adic Numbers" by F Gouvea and papers like "Equivalence of absolute values" by K Conrad and "The p-adics, Hensel's Lemma, and Newton polygons" by J Marohnic.
    
    - Summer 2016, IIIT, Hyderabad. Supervisor- Dr. Prasad Krishnan. Project Title- Index Coding with Side information using Matroid theory. This project aimed to use information and matroid theory to understand Index Coding (IC) problems with near-extreme rates and its dual. An attempt was made to convert graph theoretic results to matroid theoretic results. 
    
    - Summer 2015, NISER, Bhubaneswar. Supervisor- Dr. Shyamal Krishna De. Project Title- Measure Theoretic Approach in Probability. This project aimed to study monotone classes, sigma-algebras, random variables, expectation, and convergence of random variables from the first chapter and ten sections from the second chapter of "Probability: A Graduate Course" by Allan Gut. 
    
    - Summer 2014, NISER, Bhubaneswar. Supervisor- Dr. Brundaban Sahu. Project Title- Fields, Bases and Dimensions. This reading project aimed to study vector spaces from the first two chapters of "Finite Dimensional Vector Spaces" by Paul R. Halmos.