DMM Seminar

Speaker: Kentaro Nagao (Nagoya University)
Title: Hyperbolic 3-manifolds and Cluster Algebras
Date (JST): Mon, Apr 16, 2012, 14:00 - 17:00
Place: Seminar Room A
Abstract: Cluster algebras were invented by Fomin-Zelevinsky in their study of dual canonical bases and total positivity in semi-simple groups, and independently by Fock-Goncharov in their study of higher Teichm\"{u}ller theory. It has been discovered that the theory of cluster algebras has many links with a wide range of mathematics.

In this seminar I will show a NEW appearance of cluster algebras, which was found in a joint work with Yuji Terashima and Masahito Yamazaki. It is in explicit constructions of hyperbolic structures on the mapping tori of pseudo-Anosov mapping classes of punctured surfaces where we found cluster algebras.

In the first part, I will explain the background of the discovery. The second part will be devoted to the exhibition of the main result as well as reviews of Teichm\"{u}ller theory and hyperbolic geometry.
Remarks: Break 15:00-15:30