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Discrete mathematical modelling seminar
Seminar information archive ～04/30｜Next seminar｜Future seminars 05/01～
| Organizer(s) | Tetsuji Tokihiro, Ralph Willox |
|---|
2024/04/17
13:30-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jaume Alonso (Technische Universität Berlin)
Discrete Painlevé equations and pencils of quadrics in 3D (English)
Jaume Alonso (Technische Universität Berlin)
Discrete Painlevé equations and pencils of quadrics in 3D (English)
[ Abstract ]
In this talk we propose a new geometric interpretation of discrete Painlevé equations. From this point of view, the equations are birational transformations of $\mathbb{P}^3$ that preserve a pencil of quadrics and map each quadric of the pencil to a different one, according to a Möbius transformation of the pencil parameter. This allows for a classification of discrete Painlevé equations based on the classification of pencils of quadrics in $\mathbb{P}^3$. In this scheme, discrete Painlevé equations are obtained as deformations of the 3D QRT maps introduced in the previous talk, which consist of the composition of two involutions along the generators of the quadrics of a pencil of quadrics until they meet a second pencil. The deformation is then a birational (often linear) transformation in $\mathbb{P}^3$ under which the pencil remains invariant, but the individual quadrics do not.
This is a joint work with Yuri Suris and Kangning Wei.
In this talk we propose a new geometric interpretation of discrete Painlevé equations. From this point of view, the equations are birational transformations of $\mathbb{P}^3$ that preserve a pencil of quadrics and map each quadric of the pencil to a different one, according to a Möbius transformation of the pencil parameter. This allows for a classification of discrete Painlevé equations based on the classification of pencils of quadrics in $\mathbb{P}^3$. In this scheme, discrete Painlevé equations are obtained as deformations of the 3D QRT maps introduced in the previous talk, which consist of the composition of two involutions along the generators of the quadrics of a pencil of quadrics until they meet a second pencil. The deformation is then a birational (often linear) transformation in $\mathbb{P}^3$ under which the pencil remains invariant, but the individual quadrics do not.
This is a joint work with Yuri Suris and Kangning Wei.
