Abstract:

In 1998, Borwein, Bradley, Broadhurst and Lisonek conjectured two mysterious families of identities among the multiple zeta values (MZVs). 

In 2000, Hoffman posed a family of conjectural identities of a similar flavor on his MZV webpage. In 2016 Charlton invented "block notation" for the MZVs and beautifully unified their conjectures into two larger families, but still these conjectures remained open. In my recent work with Minoru Hirose, we discovered a curious product related to Charlton's block notation which we call the "block shuffle product" and obtained a further generalization of Charlton's conjecture. We then discovered "diamond action" which is a highly non-trivial many-variable generalization of the block shuffle product and proved the our most general conjecture by using the differential structure of the diamond action. If time permits, I'm also planning to explain about the "block associator". Using the block associator we can define the block regularized MZVs, which is the key to deal with the block shuffle identity in non-convergent case.