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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

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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.

Belongs to: Stockholm Mathematics Centre
Last changed: Nov 06, 2019