Special Seminar

Tue 15 January, 5.15pm, Michell Theatre

 

On De-Klein-ing Lie's

Yi Huang

 

Of his enormous mathematical legacy, Felix Klein is perhaps best know for his Klein bottle - an innocuous looking tube that seems to dip into itself (if you try unsuccessfully to plonk it in R^3.

 

Upon closer inspection, you realise that it's only one-sided.

 

However, perhaps unbeknownst to Klein, the Klein bottle is also a metaphor for Sophus Lie's sphere-geometry and Pl\"ucker's line-geometry - the subject of one of Klein's 1893 summer lectures in Chicago. Let's try to understand Klein's using the full force of first year linear algebra, and see why spheres and lines are really one/two side/s of the same Klein bottle.