- ku , Fukuoka 812 - 8581 Japan
نویسنده
چکیده
Classifying all algebraic solutions to the sixth Painlevé equation is an important unsettled problem. We announce some new results which might bring a new insight into this subject. The main results consist of the rationality of parameters, trigonometric Diophantine conditions, and what the author calls the Tetrahedral Theorem regarding the absence of algebraic solutions in certain situations. The method is based on fruitful interactions between the moduli theoretical formulation of Painlevé VI and dynamics on character varieties via the Riemann-Hilbert correspondence. Full details will appear elsewhere.
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