Within mathematics, I'm broadly interested in analysis, partial differential equations, and fluid mechanics. I've worked on projects related to dispersive equations including wave equations and Schrodinger equations, convex integration, general relativity, functional analysis, spectral geometry. 

Within computer science, I have worked on projects in the analysis of the Transformer architecture, datasets for language models, computer-aided reasoning, formalization.

List of publications and preprints

• S. Looi. Linking Spectral Stability to Integrated Local Energy Decay for Waves on Asymptotically Flat Spacetimes.

• S. Looi, M. Tohaneanu. Global existence and asymptotic behavior for the defocusing critical wave equation on Schwarzschild backgrounds.

• B. Dodson, S. Looi. Quantitative Scattering for the Energy-Critical Wave Equation on Asymptotically Flat Spacetimes. arXiv:2509.12424.

• S. Looi, H. Xiong. Asymptotic expansions for semilinear waves on asymptotically flat spacetimes. arXiv:2407.08997.

• S. Looi. Sharp Pointwise Decay for Quasilinear Waves on Black Hole Spacetimes. arXiv:2208.05439.

• S. Looi. Quantitative Decay for Nonlinear Wave Equations on Dynamic Spacetimes, with Sharpness for Power-Type Nonlinearities. arXiv:2207.10280.

• S. Looi. Sharp Pointwise Decay for the Energy-Critical Wave Equation on Dynamical, Asymptotically Flat Spacetimes. arXiv:2205.13197.

• S. Looi, M. Tohaneanu. Global existence and pointwise decay for nonlinear waves under the null condition, to appear in Dyn. Partial Differ. Equ. arXiv:2204.03626.

• S. Looi. Pointwise decay for the wave equation on nonstationary spacetimes. J. Math. Anal. Appl. arXiv:2105.02865.

• S. Looi, M. Tohaneanu. Scattering for critical wave equations with variable coefficients. Proc. Edinb. Math. Soc. 64(2), 298–316 (2021). arXiv:1912.06795.

• S. Looi, E. Sussman. Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients. arXiv:2407.20991.

• P. Isett, S. Looi. A proof of Onsager's Conjecture for the SQG equation. arXiv:2407.02578.

• S. Looi, D. Sher. Short-time asymptotics of the heat kernel on a curvilinear polygonal domain.

• S. Looi. Bounded Heat Transforms and the Limits of Berezin Testing on Fock Space.

• (with coauthors) AI and Polynomial Inequalities (to be released by Nov).

• (with coauthors) AI Impact on Human Proof Formalization Workflows, NeurIPS 2025.

• (with coauthors) Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning. arXiv:2412.15184.

• (with coauthors) Humanity's Last Exam. arXiv:2501.14249.

• What's the Magic Word? A Control Theory of LLM Prompting. arXiv:2310.04444. (A. Bhargava, S. Looi, C. Witkowski, M. Thomson)

• S. Looi. Some problems in quasilinear and damped wave equations. Honors Thesis, UC Berkeley (2017).