Elementary talk: Complex background of real geometry
Prof. Simon Gindikin
Rutgers University, U.S.A.
One of crucial moments of great geometry of XIX century was the question of Poncelet, why ellipses can intersect at four points but circles - their special cases- not more than at two. The answer is that there are 2 universal intersection points for all circles which are complex. I will discuss several examples (including some modern ones) when real geometry is defined by complex objects.