Greetings! Welcome to the homepage about my mathematical activities.

I completed my PhD from the The Ohio State University, Columbus in Spring 2023. Since the Fall of 2023, I have been at the Department of Mathematical Sciences at the University of Memphis in the capacity of a Postdoctoral Fellow. I am on the job market this year.

I work primarily in the field of Number Theory and Algebra but my work has enjoyed close connection with finite geometry and combinatorics recently. Mainly, I investigate instances of successes and failures of certain local-global principles:

1. My recent work concerns a local–global principle for periodic points in arithmetic dynamics. Suppose that F is a rational map and A is a finite set, all of whose points are non-periodic for F. First, this work establishes that under certain natural genericity assumption, there exist a positive density of primes p such that every point in A remains non-periodic for F modulo p. In fact, the same work presents an analogous result for finitely many rational maps F₁, F₂, … , F_n and finitely many generic sets A₁, A₂, … , A_n such that each of the A_i are non-periodic for F_i . The notion of genericity used here differs from, and is sharper than, those previously considered in the literature. Then, we establish that analogous result hold for many non-generic cases too. The article has some applications to (i) dynamical Mordell-Lang conjecture and (ii) density results on the reduction of non-torsion points simultaneously across finitely many elliptic curves.
2. Another recent submitted work establishes an analogue of local-global principle for polynomial iterates. The statement reads: Every iterate of a polynomial has local roots in almost every p-adic if and only if every iterate of that polynomial has rational roots.

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 : Mylastname.Myfirstname@memphis.edu