|Speaker :||Minking Eie (National Chung Cheng University)|
|Title :||A survey of theory of multiple zeta values|
|Time :||2021-05-21 (Fri) 15:00 - 16:00|
|Place :||Seminar Room 638, Institute of Mathematics (NTU Campus)|
In 1742, through a letter correspondence, Goldbach requested Euler to
evaluate a double series obtained from Rieman zeta function with a
finite harmonic series attached to each terms, now known as double Euler
sums. This is the beginning of multiple zeta values or r-fold Euler sums
which appeared as double Euler sums.
In 1996, Kontsevic expressed harmonic series developed by Hoffman and others from a generalization of double Euler sums, by iterated integrals over simplices. This is the modern version of multiplezeta values, appeared as integrals over simplices of sequences of differential forms of just two kinds. So their duals ( with the same value) can be obtained by changes of variables.
Now we can express multiple zeta values as well as sums of multiple zeta values as double integrals over simplices of dimension 2 or more and then proceed to evaluate some special multiple zeta values or find relations( from shuffle or stuffle) among them. There is an important theorem called sum formula obtained by Granville around 1996. Such a theorem was extended to a general form called restricted sum formula by Eie in 2009.