About

I’m Logan Bell, a PhD student in the Electrical Engineering Department at Stanford University, where I’m advised by Professor Stephen Boyd. I graduated from Stanford in 2024 with a Bachelor of Science in Mathematics and a Master of Science in Computational and Mathematical Engineering.

Research

My research focuses on first-order methods, monotone operators, automatic operator splitting, performance estimation problems (PEP), applications of optimization to pure mathematics, and statistics. I’m currently working on disciplined monotone operator programming and developing a compiler for automatic operator splitting.

Beyond my active research areas, I’m interested in number theory, algebraic geometry, probability theory, PDEs, mathematical logic, and automated theorem proving.

Why “Dual Space”?

In optimization, every primal problem has a corresponding dual problem. This blog is the dual companion to Primal Space, my professional site. Primal Space is a formal resume and portfolio, while Dual Space is for exploring ideas, sharing research notes, and discussing mathematical topics of interest.

Outside Academia

Beyond mathematics, I’m interested in philosophy, particularly metaphysics and philosophy of mind. I’m also passionate about bodybuilding, with aspirations to compete in natural bodybuilding, and I enjoy specialty coffee. I may occasionally write about these topics here.