Series of Mathematics Lectures
Title: Dilogarithm identities and cluster algebras
Speaker: Professor Tomoki Nakanishi, Nagoya University, Japan
Time: 3:30-4:30pm, Nov.1 (Wednesday) and 9:20-10:20am, Nov.3 (Friday), 2017;
Place: The Room 200-9, Mathematics Building and The Room 314, Ouyang Building,
in Yuquan Campus of Zhejiang University
The dilogarithm function was introduced by Euler. The function is especially intersting because it satisfies various functional identities, which we call dilogarithm identities.
In 1990ʻs, in the context of conformal field theory in physics, several new series of dilogarithm identities were conjectured.
However, there was no idea of how to prove the conjecture, and the origin of these identities remained to be quite mysterious.
Around 2000, a new algebraic structure called cluster algebra was introduced by Fomin and Zelevinsky. Since then it turned out gradually that the hidden cluster algebraic structure is the
origin of these conjectured identities, and the conjecture was proved by the cluster algebraic method.
In this series of talks I will explain how and why the cluster algebras solve the mystery of these dilogarithm identities.