List of publications

Analysis, PDE, Functional Analysis, Spectral Geometry, and Related Subjects

• S. Looi. Positive Toeplitz operators on pluriharmonic Fock spaces: Schatten class criteria, sharp norm comparisons, and generalized weights. arXiv.

• S. Looi. When the Berezin transform fails to detect compactness: Toeplitz operators with $L^1$ symbols on weighted Bergman spaces. arXiv.

• S. Looi. Berezin Lower Limits and Positivity Modulo Compact Operators. arXiv. 

• S. Looi. A counterexample to the Berger–Coburn conjecture. arXiv. 

• S. Looi. Unbounded symbols, heat flow, and Toeplitz operators. arXiv.

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

• B. Dodson, S. Looi. Quantitative scattering for the energy-critical wave equation on asymptotically flat spacetimes. arXiv.

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

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

• S. Looi, H. Xiong. Asymptotic expansions for semilinear waves on asymptotically flat spacetimes. Analysis and Mathematical Physics 16 (2026), no. 119. arXiv · doi.

• S. Looi. Integrable Pointwise Decay for Quasilinear Waves on Black Hole Spacetimes. arXiv. In revision at Journal of Nonlinear Waves.

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

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

• S. Looi, M. Tohaneanu. Global existence and pointwise decay for nonlinear waves under the null condition, Dyn. Partial Differ. Equ. 23 (2026), no. 3, 225–268. arXiv.

• 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.

Machine Learning

• B. Chen†, S. N. Patel†, R. Hoffmann, S. Looi*, T. Y. Yu*. Learning to coordinate symbolic tools: LLM agents for verified sum-of-squares certificates. arXiv:2608.00326. (†, *: equal contribution within each group.)

• K. M. Collins, S. Frieder, J. Bayer, J. Loader, J. Lim, P. Song, F. Zaiser, L. Zhou, S. Li, S. Looi, J. Hernandez-Orallo, J. B. Tenenbaum, C. E. Freer, U. Bhatt, A. Weller, V. Chen, I. Sucholutsky. Characterizing initial human-AI proof formalization workflows. NeurIPS Workshop on Mathematical Reasoning and AI (MATH-AI), 2025. arXiv:2606.04273.

• Center for AI Safety, Scale AI, and HLE Contributors (incl. S. Looi). A benchmark of expert-level academic questions to assess AI capabilities (Humanity's Last Exam). Nature 649 (2026), 1139–1146. arXiv:2501.14249.

• S. Frieder, J. Bayer, S. Looi, J. Loader, J. Berner, K. M. Collins, A. Juhász, F. Ruehle, S. Welleck, G. Poesia, R.-R. Griffiths, A. Weller, A. Goyal, T. Lukasiewicz, K. Buzzard, T. Gowers. Data for mathematical copilots: better ways of presenting proofs for machine learning. arXiv:2412.15184.

• A. Bhargava, S. Looi, C. Witkowski, M. Thomson. What's the magic word? A control theory of LLM prompting. arXiv:2310.04444.

Thesis

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

• S. Looi. Asymptotic behavior of hyperbolic partial differential equations. PhD Thesis, University of Kentucky (2023).