Northwestern University

2033 Sheridan Road

Evanston, IL 60208-2730

serban*at*math*dot*northwestern*dot*edu

I am primarily interested in algebraic number theory and arithmetic geometry. I will be attending the Fields Institute Thematic program on unlikely intersections, heights and efficient congruencing as a Postdoctoral Fellow January-June 2017. A more detailed CV is available upon request.

Below is information about my research-if you'd like to know more, just shoot me an e-mail!

##### Infinitesimal p-adic "Unlikely Intersection" results

As part of my thesis research, I prove a p-adic result in the spirit of the classical Manin-Mumford Conjecture. It turns out this has, among others, neat applications to the theory of Hida families over imaginary quadratic fields, which you can read about in this post by Persiflage. I am currently thinking about which settings allow for similar results and hope to uncover more interesting applications. Here is the first paper from this project:

An infinitesimal p-adic multiplicative Manin-Mumford Conjecture, (arXiv, submitted)##### Lang-Trotter Conjecture for abelian surfaces

The goal is to formulate precise analogues of the conjecture for elliptic curves by Lang and Trotter in the case of abelian surfaces. One studies the density of primes for which the trace of Frobenius acting on torsion points is a fixed integer. If the image of Galois is big, i.e. has finite index in GSp(4), this has been worked out recently here. However, contrary to elliptic curves, there are now many remaining cases to consider in which interesting things happen! I am writing a paper with Hao Chen, Alina Cojocaru, Nathan Jones and Daniel Miller where we examine some of the subtleties that occur for pairs of non-CM elliptic curves, formulate a precise conjecture and gather numerical evidence.