Oriented lines in 3-space

Motivated by the study of the amplituhedron in physics, we are interested in the relative position of lines in the real 3-space. Given two oriented lines, they can intersect, be positively oriented or be negatively oriented. In this talk, I will explore which combinations of these three possibilities can be seen in a larger set of oriented lines. After establishing connections of lines in 3-space with rigidity theory and spectral graph theory, I will apply tools from these areas to lines.