Khazhgali Kozhasov: On the number of critical points of a real form on the sphere
Time: Wed 2019-11-27 13.15 - 14.15
Location: Kräftriket, house 6, room 306
Participating: Khazhgali Kozhasov, TU Braunschweig
It is well-known that a generic real symmetric matrix of size n has exactly n real eigenvalues. Equivalently, a generic real quadratic form in n variables restricted to the unit sphere S has exactly n critical points. But, if p is a real form (homogeneous polynomial) of degree \(d\geq 3\), the number C(p) of critical points of its restriction to the sphere S is not generically constant. In my talk I will describe typical values of the number C(p) that a generic p can attain.