# Khazhgali Kozhasov: On the number of critical points of a real form on the sphere

**Time: **
Wed 2019-11-27 13.15 - 14.15

**Lecturer: **
Khazhgali Kozhasov, TU Braunschweig

**Location: ** Kräftriket, house 6, room 306

### Abstract

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.