Research

Currently, I'm working on Brauer-Manin obstruction to Weak approximation on certain Kummer surfaces. In particular, products of complex multiplication elliptic curves. Before that, I worked on rational points on elliptic curves, particularly on the ranks of elliptic curves over the field of rationals. 

Publications

• M. Alaa Tawfik, R. Newton. Transcendental Brauer-Manin obstructions on singular K3 surfaces, submitted to Research in Number Theory. https://arxiv.org/abs/2311.00650 

• High rank quadratic twists of pairs of elliptic curves , joint with Mohammad Sadek. Journal of Number Theory, Volume 174 (2017), 436-444 .

• On geometric progressions on hyperelliptic curves, joint with Mohammad Sadek. Journal of Integer Sequences, Volume 19 (2016), Article 16.6.3.

Master's Thesis

Elliptic Surfaces with positive Mordell-Weil rank and Quadratic twists of elliptic curves. Cairo University, 2017.