I work in analysis/partial differential equations (PDEs), fluid mechanics, and formal verification. In nonlinear wave equations on asymptotically flat and black-hole spacetimes, my results established decay, asymptotics, scattering, and existence. In fluid dynamics, P. Isett and I resolved the Onsager conjecture for the surface quasi-geostrophic (SQG) equation. I work on problems in spectral geometry and functional analysis; stability mechanisms for incompressible and geophysical flows — especially inviscid damping and related phenomena; and classical dispersive models such as linear wave and Schrödinger equations.

A second line of work applies proof assistants to problems in analysis and polynomial inequalities. I build a proof engine and supporting infrastructure with collaborators; contributed to the Lean 4 formalization of PDEs; curate and clean math datasets; and studied transformer architectures. I also led a team at Project Numina (winner of the 2024 AIMO Prize), developing end-to-end pipelines for formal and automated reasoning in mathematics.

List of publications and preprints

• S. Looi, D. Sher. The Dirichlet heat trace for domains with curved corners.

• 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.

• (with coauthors) AI and Polynomial Inequalities

• (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. (v2: 2025+)

• (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).