18 citations · 20 across the 6 of their papers we have counts for
7 papers
The heat trace for domains with curved corners
Sam Looi, David Sher
The heat trace of a planar polygon contains corner terms depending only on the opening angles, while the heat trace of a smooth planar domain contains curvature terms along the bou…
Asymptotic expansions for semilinear waves on asymptotically flat spacetimes
Sam Looi, Haoren Xiong
We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. Our analysis focuses on two…
Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients
Shi-Zhuo Looi, Ethan Sussman
Using the recent analysis of the output of the low-energy resolvent of Schrödinger operators on asymptotically conic manifolds (including Euclidean space) when the potential is sh…
Quantitative Scattering for the Energy-Critical Wave Equation on Asymptotically Flat Spacetimes
Benjamin Dodson, Sam Looi
We prove quantitative scattering for the three-dimensional defocusing energy-critical quintic wave equation on a class of asymptotically flat, possibly non-stationary perturbations…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1144
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
Global existence and pointwise decay for nonlinear waves under the null condition
Shi-Zhuo Looi, Mihai Tohaneanu
This paper proves global existence and sharp pointwise decay for solutions to nonlinear wave equations satisfying the semilinear null condition, on a class of three-dimensional, as…