Derived Geometry and Non-Linear Differential Equations on the Punctured Disc

2022/02/13 by Emile Bouaziz, Bouaziz, Emile
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2202.06398

openalex publication_date 2022/02/13 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of variations, we show that a variational formulation of a differential equation is equivalent to the residue pairing inducing a (-1)-symplectic form on the derived space of solutions equipped with a certain decoration of its tangent complex.

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