An algebraic geometry question and wave turbulence

TL;DR

This paper proposes an algebraic geometry conjecture and explores its implications for wave turbulence theory, linking number theory and analysis to advance understanding in the field.

Contribution

It introduces a new algebraic geometry conjecture and demonstrates its potential to impact wave turbulence research.

Findings

Formulation of a natural algebraic geometry conjecture

Derivation of number theoretic and analytical consequences

Application of these consequences to advance wave turbulence theory

Abstract

This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.