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Cohomological geometry of differential equations
January 8, 2025 19:20, Moscow, online, for the access link please contact seminar@gdeq.org

Towards a theory of homotopy structures for differential equations: First definitions and examples. Part 2

V. N. Rubtsov



Abstract: We define $A_\infty$-algebra structures on horizontal and vertical cohomologies of (formally integrable) partial differential equations.
Since higher order $A_\infty$-algebra operations are related to Massey products, our observation implies the existence of invariants for differential equations that go beyond conservation laws.
We also propose notions of formality for PDEs, and we present examples of formal equations.

Language: English

Website: https://doi.org/10.1016/j.jde.2024.08.057
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