Zusammenfassung für den Vortrag am 25.04.2017 (11:00 Uhr)Seminar on Nonlinear Algebra
Alexander Bobenko (Technische Universität Berlin)
On a discretization of confocal quadrics: Geometric parametrizations, integrable systems and incircular nets
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Confocal quadrics lie at the heart of the system of confocal coordinates (also called elliptic coordinates). We suggest a geometric discretization which leads to factorisable discrete nets with a novel discrete analog of the orthogonality property and to an integrable discretization of the Euler-Poisson-Darboux equation. The coordinate functions of discrete confocal quadrics are computed explicitly. We demonstrate that special discrete confocal conics lead to incircular nets. This is a joint work with W. Schief, Yu. Suris and J. Techter