Zach Abdulrahman

I am an applied mathematician working at the interface of optimization, numerical analysis, and dynamical systems. I am currently an M.S. student in the Applied Mathematics thesis track at NYU’s Courant Institute, where my thesis is advised by David McLaughlin.

On the optimization side, I developed ADRS-M, an accelerated Douglas–Rachford splitting method for nonsmooth convex problems that uses a monotone residual restart to guarantee a nonincreasing fixed-point residual. As a visiting researcher in the Schaffer Lab at Mount Sinai, I study how gradient clipping shapes the training dynamics of recurrent neural networks, including transfer and task-feature learning.

My M.S. thesis develops phenomenological dynamical-systems models of PP1/PP2A regulation of LTP/LTD, focusing on the bifurcation structure that governs hippocampal plasticity.

Together, these directions motivate my interest in learning-based numerical methods — particularly understanding neural operators through their approximation guarantees and optimization behavior, with applications to PDEs arising in biological systems.

Before Courant, I completed a B.S. in Computer Science and Mathematics at the University of South Carolina, where I worked on generalized leaky integrate-and-fire network models with Yi Sun.