Department of Mathematics

Dr. Alexander Goncharov, Department of Mathematics, Yale University

Abstract: The logarithm is unique, up to a multiplicative constant,  continuous function satisfying the addition law:ln (xy)= ln x + ln y. It is also the integral of dt/t from 1 to x.

The quest for understanding of integrals was and is one of the main driving forces behind the development of Math.The theory of one dimensional integrals of algebraic functions of one variable was created by Abel.The theory of addition laws for these integrals is known now under the hat of algebraic curves and their Jacobians.

Polylogarithms are a different way to generalize the logarithm.The dilogarithm  was invented by Leibniz in 1696.Abel discovered the  addition law for the dilogarithm, but its role and meaning was understood and appreciated only in 1970's.Since then polylogarithm played an ever growing role  in Mathematics and Physics.However their properties are still very  mysterious.

I will review what we know about polylogarithms and their functional equation, and what we don't.

Zoom Meeting

Meeting ID: 991 7926 6453

Passcode:  396836