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**第2回 [#k4d4881e]

日 時 : 1月29日(水) 14:00〜15:00

講演者 : Ser Peow Tan 氏 (東工大情報理工)

場 所 : W 809 号室

題 目 : Right-angled Hexagons in hyperbolic 3-space: Variations on a theme

要 約 : 

There are many trigonometric identities for polygons in the hyperbolic plane, many of which look extremely similar, for example the sine law for the triangle and the sine law for the right-angled hexagon. The main theme of this talk is to look at certain basic configurations in hyperbolic 3-space, namely the right angled hexagons, and show that they satisfy the laws of Sines and Cosines. We then explore variations of this theme, showing how this can be used to unify or generalize various aspects of hyperbolic geometry, namely:

・ Polygons in the hyperbolic plane - we show that the trigonometric identities for polygons in the hyperbolic plane can be deduced from these two basic laws.

・ Fenchel-Nielsen coordinates - we show that the Fenchel-Nielsen coordinates for Teichmuller space, which are built from right angled hexagons in the plane, can be generalized to Fenchel-Nielsen coordinates for quasi-fuchsian space.

・ Variational formulae - we give a variational formula which arises from the study of disk patterns in the hyperbolic plane, and show how this can be complexified using right angled hyperbolic hexagons in 3-space.

**第1回 [#w1357b08]

日 時 : 11月20日(水) 14:00〜15:00

講演者 : 北野 晃朗 氏 (東工大情報理工)

場 所 : W 809 号室

題 目 : ファイバー結び目とアレキサンダー多項式について

要 約 : 

(東京農工大 合田氏、森藤氏との共同研究)