Vlad Serban

Welcome!

I am an Assistant Professor of Mathematics at New College of Florida.

Before Florida, I was a postdoc at EPFL working with Prof. Maryna Viazovska. My research interests lie in algebraic number theory and a good chunk of my work is related to p-adic aspects of the Langlands programme. I also enjoy thinking about how to apply ideas from arithmetic to cryptography and various optimization problems such as the sphere packing problem.

You can find some of my work below, stay tuned for upcoming work on p-adic L-functions and results on packing and covering.

Contact: vmy_last_name@ncf(dot)edu

Papers and preprints

Effective module lattices and their shortest vectors, with Nihar Gargava, Maryna Viazovska and Ilaria Viglino. arXiv:2402.10305
Moments of the number of points in a bounded set for number field lattices, with Nihar Gargava and Maryna Viazovska. arXiv:2308.15275
Non-vanishing of critical L-values in Hida families, with Rob Pollack. arXiv:2208.02769
Unlikely intersections on the p-adic formal ball. arXiv:2107.06610 Res. Number Theory (2023), vol. 9 (34), https://doi.org/10.1007/s40993-023-00441-1.
Dense packings via lifts of codes to division rings, with Nihar Gargava. arXiv:2111.03684 IEEE Trans. Inform. Theory (2023), vol. 69, no. 5, pp. 2860-2873, https://doi.org/10.1109/TIT.2022.3226028.
On p-adic versions of the Manin-Mumford Conjecture. arXiv:2007.02069 Int. Math. Res. Not. IMRN (2022), no.13, 10279-10301, https://doi.org/10.1093/imrn/rnab136.
The Lang-Trotter conjecture for products of non-CM elliptic curves, with Hao Chen and Nathan Jones. arXiv:2006.11269 Ramanujan J. (2022), vol. 59, pp. 379-436, https://doi.org/10.1007/s11139-021-00543-3.
A finiteness result for p-adic families of Bianchi modular forms. arXiv:1902.03217 J. Number Theory (2021), vol. 233, pp. 405-431, https://doi.org/10.1016/j.jnt.2021.06.016.
An infinitesimal p-adic multiplicative Manin-Mumford Conjecture. arXiv:1607.01428 J. Théor. Nombres Bordeaux (2018), vol. 30, no.2, pp. 393-408, https://doi.org/10.5802/jtnb.1030.

Other resources

As part of the "Bianchi" paper above, I wrote some MAGMA code to compute with Bianchi modular forms with Nebentypus. If you are interested, feel free to message me.

Here is my google scholar page. A detailed CV is also available upon request.