Luis Crespo

activity

20232026

collaborators

9 papers

math.SG2026

The contrast between real and $p$ -adic integrability

Luis Crespo, Álvaro Pelayo

A fundamental question in $p$ -adic symplectic geometry and $p$ -adic Hamiltonian mechanics is to what extent we can learn new information about integrable systems with coefficients…

math.SG2026

$p$ -adic symplectic geometry of integrable systems and Weierstrass-Williamson theory II

Luis Crespo, Álvaro Pelayo

This paper is a sequel to arXiv:2501.14444, in which we shall give proofs of several results stated in arXiv:2501.14444 (Theorems D--L) which, for brevity and clarity, we postponed…

math.SG2025

Group actions on $p$ -adic symplectic manifolds

Luis Crespo, Álvaro Pelayo

Let $p$ be a prime number. We introduce symplectic actions of $p$ -adic analytic Lie groups on $p$ -adic symplectic manifolds. Then we show that any $p$ -adic symplectic action $G\tim…

math.SG2025

$p$ -adic angular momentum coupling in symplectic geometry

Luis Crespo, Álvaro Pelayo

The coupled angular momentum is an integrable system with two degrees of freedom which is fundamental in physics and the theory of integrable systems. It is obtained by coupling tw…

math.SG2025

Darboux's Theorem in $p$ -adic symplectic geometry

Luis Crespo, Álvaro Pelayo

We prove a non Archimedean Darboux's Theorem: any two symplectic forms on a $p$ -adic analytic manifold are locally isomorphic. Understanding local problems such as the existence of…

math.SG2025

Rigidity and flexibility in $p$ -adic symplectic geometry

Luis Crespo, Álvaro Pelayo

Let $n \geq 2$ be an integer and let $p$ be a prime number. We prove that the analog of Gromov's non-squeezing theorem does not hold for $p$ -adic embeddings: for any $p$ -adic absolut…

math.SG2025

$p$ -adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I

Luis Crespo, Álvaro Pelayo

The local symplectic theory of integrable systems is fundamental to understand their global theory, as well as the behavior near singularities of fundamental models from classical…

math.SG2024

The $p$ -adic Jaynes-Cummings model in symplectic geometry

Luis Crespo, Álvaro Pelayo

The notion of classical $p$ -adic integrable system on a $p$ -adic symplectic manifold was proposed by Voevodsky, Warren and the second author a decade ago in analogy with the real c…

math.CO2023

Ewald's Conjecture and integer points in algebraic and symplectic toric geometry

Luis Crespo, Álvaro Pelayo, Francisco Santos

We solve several open problems concerning integer points of polytopes arising in symplectic and algebraic geometry. In this direction we give the first proof of a broad case of Ewa…

The contrast between real and p-adic integrability

p-adic symplectic geometry of integrable systems and Weierstrass-Williamson theory II

Group actions on p-adic symplectic manifolds

p-adic angular momentum coupling in symplectic geometry

Darboux's Theorem in p-adic symplectic geometry

Rigidity and flexibility in p-adic symplectic geometry

p-adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I

The p-adic Jaynes-Cummings model in symplectic geometry

Ewald's Conjecture and integer points in algebraic and symplectic toric geometry

The contrast between real and $p$ -adic integrability

$p$ -adic symplectic geometry of integrable systems and Weierstrass-Williamson theory II

Group actions on $p$ -adic symplectic manifolds

$p$ -adic angular momentum coupling in symplectic geometry

Darboux's Theorem in $p$ -adic symplectic geometry

Rigidity and flexibility in $p$ -adic symplectic geometry

$p$ -adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I

The $p$ -adic Jaynes-Cummings model in symplectic geometry