Arithmetic Study Group: The coproduct on multiple zeta values, and `almost' identities
20 October 2015 14:00 in CM103
Multiple zeta values are a mysterious and intriguing set of real numbers, about which many results are conjectured, but relatively little is proven. One is typically interested in finding all relations between MZVs, and completely understanding them, but transcendentality problems make this difficult to approach directly. One way to make progress with these questions is by lifting MZVs to purely algebraic objects which have additional, more rigid, structure.
I will start by giving an introduction to MZVs and some of the various standard results about them. From here we will lift to Brown's motivic MZVs, and look at the coproduct structure they acquire. Then using this coproduct, I will show how one can sometimes get easy combinatorial proofs of `almost' identities (identities up to a non-explicit rational), even in cases where the explicit identity remains conjectural.
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