Discrete Laplace-Darboux sequences, Menelaus' theorem and the pentagram map
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| Description: |
Wolfgang K. Schief (TU Berlin)
Friday 03 April 2009, 09:30-10:15 Geometric Aspects of Discrete and Ultra-discrete Integrable Systems |
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| Created: | 2011-03-10 13:15 | ||||||||
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| Collection: | Discrete Integrable Systems | ||||||||
| Publisher: | Isaac Newton Institute | ||||||||
| Copyright: | Wolfgang K. Schief | ||||||||
| Language: | eng (English) | ||||||||
| Distribution: |
World
(downloadable)
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| Explicit content: | No | ||||||||
| Aspect Ratio: | 4:3 | ||||||||
| Screencast: | No | ||||||||
| Bumper: | UCS Default | ||||||||
| Trailer: | UCS Default | ||||||||
| Abstract: | A seminar from the Geometric Aspects of Discrete and Ultra-discrete Integrable Systems conference in association with the Newton Institute programme: Discrete Integrable Systems
http://www.gla.ac.uk/departments/mathematics/research/isamp/events/gadudis/programme/ The discrete analogue of the classical notion of Laplace-Darboux sequences of conjugate nets was introduced by Doliwa. In view of the associated classification problem, we take a fresh look at this topic and re-formulate the theory in terms of the multi-ratio condition associated with Menelaus' theorem. As an application, we demonstrate that the pentagram map analysed in detail by Ovsienko, Schwartz and Tabachnikov may be regarded as a particular Laplace-Darboux sequence leading to a (non-standard) discrete version of the Schwarzian Boussinesq equation. |
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