Greetings! Welcome to the homepage about my mathematical activities.

I was a postdoctoral fellow in the Department of Mathematical Sciences at the University of Memphis from Aug, 2023 to Jul, 2026. Before that, I was a PhD candidate in the Department of Mathematics at the Ohio State University from Aug, 2017 to May, 2023. I completed my undergraduate in Mathematics from Berea College, KY in Aug, 2017.

My MR author ID is 1438156. My ORCID and zbMATH author ID can be accessed respectively by clicking here and here. The best way to reach me is through email at : (myfirstname)(mylastname)2024@gmail.com

I work primarily at the interface of number theory and algebra. My research investigates instances of successes and failures of certain local-global principles in number theory. This also involves using local methods to address a wide class of number-theoretic problems. My research has entered an especially exciting phase and I am excited to share the following selection of my recent works.

My most recently submitted works are about the dynamical Mordell-Lang conjecture. In particular, in one of the manuscript, we confirm the conjecture for arbitrary endomorphisms of products of smooth projective curves and what is known as relatively Etale systems over such products. You can access the preprint of this work by clicking HERE.

Likewise, another recently submitted work establishes the conjecture for higher-rank radially ramified skew products in arbitrary dimensions and arbitrary fiber rank. This same work also gives an application in the form of a uniform Skolem-Mahler-Lech theorem for a fixed nonlinear orbit and a fixed polynomial-coefficient linear recurrence. You can access the preprint associated with this work by clicking HERE.

Another recently submitted work of mine is about reverse-sparsity principles associated with polynomial factorization. In this work, we prove existence of infinitely many polynomials with exactly \(m\) non-zero coefficients – each irreducible factor of which has at least superpolynomially many (in \(m\)) nonzero coefficients. This places polynomial factorization in a radically different category as compared to other algebraic operations such as composition, taking powers of polynomials etc. for which reverse-sparsity principles were affirmately established by Schinzel, by Erdős, by Fuchs, Zannier and several others. This same result also concerns a weaker constant \(K(m)\) defined by Schinzel who showed with Choudhry that \(K(m) > \text{max} \big\{2m, 0.014m^{1.22} \}\) using a result of Verdenius. Our result implies that \(K(m)\) is eventually larger than any polynomial in \(m\). You can see a preprint of this work by clicking HERE.