Dept Math & Stat UiT, Forskningsparken B459
  29 Aug 10:15-12:00

Matous Trnka (Masaryk University Brno)

"Lines in RP^3 via homogeneous spaces and Plucker embedding"

In this talk we will examine the geometry structure of the space of lines in three dimensions. We will use results from the theory of homogeneous spaces G/P and spaces with indefinite metric signature. If there is enough time, we will also investigate curves in this space, a.k.a. ruled surfaces. Particularly we will ask what quantities describe a ruled surface uniquely up to a specific group of symmetries and what surfaces with these quantities being constant look like.