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Hajime Nagoya

2015-05-12
14:00:00 - 15:30:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

In the first part, I will explain basic facts of the conformal blocks, which are building blocks of the correlation functions of the two dimensional conformal field theory. Then, I will review on the Fourier expansion of the tau function of the sixth Painleve function discovered by Gamayun, Iorgov and Lisovyy.

In the second part, irregular versions of the conformal blocks will be discussed. Using irregular conformal blocks which are series expansions at an irregular singular point, conjectural formulas of Fourier expansions of the tau functions of the fifth and fourth Painleve functions will be given. Note that although the Fourier expansions of the tau functions of the fifth and third Painleve fucntions in terms of irregular conformal blocks were obtained by Gamayun, Iorgov and Lisovyy, they are expansions at regular singular points.

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