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 forthcoming professional site. Primal Space will be 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 hypertrophy training, and I enjoy specialty coffee. I may occasionally write about these topics here.