11 papers
The energy of fractional Allen--Cahn layers in dimension one
Alvaro Carballeira, Damien Galant, Javier Gómez-Serrano
We study the energy of the one-dimensional fractional Allen--Cahn layer solution , defined as the unique odd, increasing solution of $(-Δ)^{s} Φ…
Linear instability of a Burgers--Hilbert traveling wave
Ãngel Castro, Javier Gómez-Serrano, Miguel M. G. Pascual-Caballo
We study the stability of traveling wave solutions to the Burgers--Hilbert equation on in the regime of small frequency and large wave speed . For and…
Nested nodal loops of biharmonic functions
Javier Gómez-Serrano, Robert Koirala, Alexander Logunov
Given any \(n\in\mathbb{N}\), we construct a real-valued biharmonic polynomial on \(\mathbb{R}^2\) whose zero set contains a nest of \(n\) smooth, disjoint topological loops, meani…
Monotonicity of the first Dirichlet eigenvalue of regular polygons
Joel Dahne, Javier Gómez-Serrano, Joana Pech-Alberich
In this paper we prove that the first Dirichlet eigenvalue of an -sided regular polygon of fixed area is a monotonically decreasing function of for all ,…
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…
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…