Arithmetic Study Group: Polylogarithms and Double Scissors Congruence Groups
18 February 2014 13:00 in CM107
Polylogarithms are a class of special functions which have applications throughout the mathematics and physics worlds. I will begin by introducing the basic properties of polylogarithms and some reasons for interest in them, such as their functional equations and the role they play in Zagier's polylogarithm conjecture. From here I will turn to Aomoto polylogarithms, a more general class of functions and explain how they motivate a geometric view of polylogarithms as configurations of hyperplanes in P^n. This approach has been used by Goncharov to establish Zagier's conjecture for n = 3.
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