Seminar talk, 8 January 2025: Difference between revisions
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Created page with "{{Talk | speaker = Vladimir Rubtsov | title = Towards a theory of homotopy structures for differential equations: First definitions and examples. Part 2 | abstract = We define <math>A_\infty</math>-algebra structures on horizontal and vertical cohomologies of (formally integrable) partial differential equations. Since higher order <math>A_\infty</math>-algebra operations are related to Massey products, our observation implies the existence of invariants for differentia..." |
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| speaker = Vladimir Rubtsov | | speaker = Vladimir Rubtsov | ||
| title = Towards a theory of homotopy structures for differential equations: First definitions and examples. Part 2 | | title = Towards a theory of homotopy structures for differential equations: First definitions and examples. Part 2 | ||
| abstract = We define <math>A_\infty</math>-algebra structures on horizontal and vertical cohomologies of (formally integrable) partial differential equations. | | abstract = A continuation of the talk [[Seminar talk, 18 December 2024|on 18 December]]. | ||
We define <math>A_\infty</math>-algebra structures on horizontal and vertical cohomologies of (formally integrable) partial differential equations. | |||
Since higher order <math>A_\infty</math>-algebra operations are related to Massey products, our observation implies the existence of invariants for differential equations that go beyond conservation laws. | Since higher order <math>A_\infty</math>-algebra operations are related to Massey products, our observation implies the existence of invariants for differential equations that go beyond conservation laws. | ||
Revision as of 15:38, 1 January 2025
Speaker: Vladimir Rubtsov
Title: Towards a theory of homotopy structures for differential equations: First definitions and examples. Part 2
Abstract:
A continuation of the talk on 18 December.
We define -algebra structures on horizontal and vertical cohomologies of (formally integrable) partial differential equations.
Since higher order -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.
References:
https://doi.org/10.1016/j.jde.2024.08.057