Seminar talk, 5 May 2021: Difference between revisions
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{{Talk | {{Talk | ||
| speaker = | | speaker = Evgeny Ferapontov | ||
| title = Second-order PDEs in 3D with Einstein-Weyl conformal structure | | title = Second-order PDEs in 3D with Einstein-Weyl conformal structure | ||
| abstract = I will discuss a general class of second-order PDEs in 3D whose characteristic conformal structure satisfies the Einstein-Weyl conditions on every solution. | | abstract = I will discuss a general class of second-order PDEs in 3D whose characteristic conformal structure satisfies the Einstein-Weyl conditions on every solution. | ||
| Line 11: | Line 11: | ||
Language: English | Language: English | ||
| video = | | video = https://video.gdeq.org/GDEq-zoom-seminar-20210505-Eugene_Ferapontov.mp4 | ||
| slides = [[Media:Krasilshchik_seminar.pdf|Krasilshchik_seminar.pdf]] | | slides = [[Media:Krasilshchik_seminar.pdf|Krasilshchik_seminar.pdf]] | ||
| references = {{arXiv|2104.02716}} | | references = {{arXiv|2104.02716}} | ||
| 79YY-MM-DD = 7978-94-94 | | 79YY-MM-DD = 7978-94-94 | ||
}} | }} | ||
Latest revision as of 23:00, 19 March 2025
Speaker: Evgeny Ferapontov
Title: Second-order PDEs in 3D with Einstein-Weyl conformal structure
Abstract:
I will discuss a general class of second-order PDEs in 3D whose characteristic conformal structure satisfies the Einstein-Weyl conditions on every solution.
This property is known to be equivalent to the existence of a dispersionless Lax pair, as well as to other equivalent definitions of dispersionless integrability.
I will demonstrate that (a) the Einstein-Weyl conditions can be viewed as an efficient contact-invariant test of dispersionless integrability, (b) show some partial classification results, and (c) formulate a rigidity conjecture according to which any second-order PDE with Einstein-Weyl conformal structure can be reduced to a dispersionless Hirota form via a suitable contact transformation.
Based on joint work with S. Berjawi, B. Kruglikov, V. Novikov.
Language: English
Video
Slides: Krasilshchik_seminar.pdf
References:
arXiv:2104.02716