Text only print
Full screen print
Infinite Analysis Seminar Tokyo
Seminar information archive ～10/06｜Next seminar｜Future seminars 10/07～
| Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|
2024/10/16
15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Davide Dal Martello (Rikkyo University)
Convolutions, factorizations, and clusters from Painlevé VI (English)
Davide Dal Martello (Rikkyo University)
Convolutions, factorizations, and clusters from Painlevé VI (English)
[ Abstract ]
The Painlevé VI equation governs the isomonodromic deformation problem of both 2-dimensional Fuchsian and 3-dimensional Birkhoff systems. Through duality, this feature identifies the two systems. We prove this bijection admits a more transparent middle convolution formulation, which unlocks a monodromic translation involving the Killing factorization. Moreover, exploiting a higher Teichmüller parametrization of the monodromy group, Okamoto's birational map of PVI is given a new realization as a cluster transformation. Time permitting, we conclude with a taste of the quantum version of these constructions.
The Painlevé VI equation governs the isomonodromic deformation problem of both 2-dimensional Fuchsian and 3-dimensional Birkhoff systems. Through duality, this feature identifies the two systems. We prove this bijection admits a more transparent middle convolution formulation, which unlocks a monodromic translation involving the Killing factorization. Moreover, exploiting a higher Teichmüller parametrization of the monodromy group, Okamoto's birational map of PVI is given a new realization as a cluster transformation. Time permitting, we conclude with a taste of the quantum version of these constructions.
