The dilogarithm function was introduced by Euler, and the function and its variations appear in several areas of mathematics, e.g., hyperbolic geometry, algebraic K-theory, conformal field theory, integrable systems. The function is remarkable in the sense that it satisfies a great variety of functional equations, including the celebrated pentagon identity, which we call dilogarithm identities. On the other hand, cluster algebras, introduced by Fomin and Zelevinsky around 2000, are a rather recently introduced combinatorial/algebraic structure originated in Lie theory. It was not originally intended, but it turns out that the dilogarithm is ``build-into” the cluster algebra structure as the Hamiltonian. In this talk I explain how the dilogarithm identity associated with a period of mutations in a cluster algebra arises especially from Hamiltonian/Lagrangian point of view. (Based on the joint work with M. Gekhtman and D. Rupel.)

Date

2019/11/13 Wed 14:45 - 15:45

Room

Room 110, Building No.3

Speaker

Tomoki Nakanishi

Affiliation

Nagoya University

Abstract