Colored Multiple Zeta Values


Jianqiang Zhao ( Eckerd college, USA )
2016-03-04  10:30 - 11:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

Multiple polylogarithms are multiple variable generalizations of the polylogarithms which are in turn generalizations of the logarithm function. Their special values at Nth roots of unity are called colored multiple zeta values (CMZVs) of level N. In recent year, CMZVs have appeared in many area in mathematics and theoretical physics alike. In this talk I will start by reviewing the fundamental properties and key questions concerning CMZVs. Then I will consider their symmetrized and finite analogs and provide a link between them based on some extensive numerical computation. In order to explain these data, we will need to define a p-adic analog of the CMVZs which is still under development. This work is partially joint with J. Singer.