The Painlevé III equation of type (0,0,4,-4), associated vector bundles with additional structure, and the geometry of the movable poles of real solutions
16:50:00 - 17:40:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
In 1986 Its and Novokshenov studied the asymptotics and the movable poles of real solutions on the real positive line of the Painlevé III equation of type (0,0,4,-4). They had results on the behaviour near 0 and near infinity. I will talk about the global geometry of the movable poles for all solutions together. This will lead to facts on the movable poles (and movable zeros) on the whole positive real line. Behind this is an interpretation of the corresponding isomonodromic connections as TERP-structures (or noncommutative Hodge structures) and results on them by T. Mochizuki, Sabbah and myself. I will also talk about the vector bundles with connections and additional structures, which are behind complex multi-valued solutions on C*. The results are joint work with M.A. Guest.