Title: Multiple Polylogarithms in Weight 4
Speaker: Herbert Gangl
Date: Tuesday, November 19, 2013
Time: 11:00am – 12:30pm
Place: Seminar Room 313, Simons Center
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Abstract: It is well-known that all multiple polylogarithms of weight 2 and 3 are expressible in terms of Li_2 and Li_3, respectively, while the interplay between the weight 4 functions is considerably more complicated–in particular, they are not all expressed in terms of Li_4.
We give some of the first functional equations among weight 4 polylogarithms, involving in particular Li_{2,2}, Li_{3,1} and Li_{1,1,1,1}. We are also led to a functional equation in 4 variables for Li_4 which should play an important role in an explicit definition of the corresponding higher Bloch group.