Seminar talk, 17 December 2025: Difference between revisions
Created page with "{{Talk | speaker = Evgeny Ferapontov | title = Involutive scroll structures on solutions of 4D dispersionless integrable hierarchies | abstract = A rational normal scroll structure on an (n+1)-dimensional manifold M is defined as a field of rational normal scrolls of degree n-1 in the projectivised cotangent bundle PT*M. We show that geometry of this kind naturally arises on solutions of various 4D dispersionless integrable hierarchies of heavenly type equations...." |
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| speaker = Evgeny Ferapontov | | speaker = Evgeny Ferapontov | ||
| title = Involutive scroll structures on solutions of 4D dispersionless integrable hierarchies | | title = Involutive scroll structures on solutions of 4D dispersionless integrable hierarchies | ||
| abstract = A rational normal scroll structure on an (n+1)-dimensional manifold M is defined as a field of rational normal scrolls of degree n-1 in the projectivised cotangent bundle PT*M. | | abstract = A rational normal scroll structure on an (n+1)-dimensional manifold M is defined as a field of rational normal scrolls of degree n-1 in the projectivised cotangent bundle <math>PT^*M</math>. | ||
We show that geometry of this kind naturally arises on solutions of various 4D dispersionless integrable hierarchies of heavenly type equations. In this context, rational normal scrolls coincide with the characteristic varieties (principal symbols) of the hierarchy. Furthermore, such structures automatically satisfy an additional property of involutivity. | We show that geometry of this kind naturally arises on solutions of various 4D dispersionless integrable hierarchies of heavenly type equations. In this context, rational normal scrolls coincide with the characteristic varieties (principal symbols) of the hierarchy. Furthermore, such structures automatically satisfy an additional property of involutivity. | ||
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Based on joint work with Boris Kruglikov. | Based on joint work with Boris Kruglikov. | ||
| video = | | video = https://video.gdeq.org/GDEq-zoom-seminar-20251217-Evgeny_Ferapontov.mp4 | ||
| slides = | | slides = [[Media:Fer_Krasil'shchik_sem.pdf|Fer_Krasil'shchik_sem.pdf]] | ||
| references = {{arXiv|2503.10897}} | | references = {{arXiv|2503.10897}} | ||
| 79YY-MM-DD = 7974-87-82 | | 79YY-MM-DD = 7974-87-82 | ||
}} | }} | ||
Latest revision as of 00:01, 18 December 2025
Speaker: Evgeny Ferapontov
Title: Involutive scroll structures on solutions of 4D dispersionless integrable hierarchies
Abstract:
A rational normal scroll structure on an (n+1)-dimensional manifold M is defined as a field of rational normal scrolls of degree n-1 in the projectivised cotangent bundle .
We show that geometry of this kind naturally arises on solutions of various 4D dispersionless integrable hierarchies of heavenly type equations. In this context, rational normal scrolls coincide with the characteristic varieties (principal symbols) of the hierarchy. Furthermore, such structures automatically satisfy an additional property of involutivity.
Our main result states that involutive scroll structures are themselves governed by a dispersionless integrable hierarchy, namely, the hierarchy of conformal self-duality equations.
Based on joint work with Boris Kruglikov.
Video
Slides: Fer_Krasil'shchik_sem.pdf
References:
arXiv:2503.10897