68 citations · 351 across the 40 of their papers we have counts for
4 papers · 1 filter
Mathematical exploration and discovery at scale
Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao +1
AlphaEvolve (Novikov et al., 2025) is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary f…
Homogeneous steady states for the generalized surface quasi-geostrophic equations
Ken Abe, Javier Gómez-Serrano, In-Jee Jeong
We consider homogeneous (stationary self-similar) solutions to the generalized surface quasi-geostrophic (gSQG) equations parametrized by the constant , representing the 2D…
Discovery of Unstable Singularities
Yongji Wang, Mehdi Bennani, James Martens +19
Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Eul…
A note on the existence of self-similar profiles of the hydrodynamic formulation of the focusing nonlinear Schrödinger equation
Gonzalo Cao-Labora, Javier Gómez-Serrano, Jia Shi +1
After performing the Madelung transformation, the nonlinear Schrödinger equation is transformed into a hydrodynamic equation akin to the compressible Euler equations with a certain…