Abstract for the talk on 30.04.2020 (18:20 h)Nonlinear Algebra Seminar Online (NASO)
Khazhgali Kozhasov (Technical University Braunschweig)
On Minimality of Determinantal Varieties
See the video of this talk.
Minimal submanifolds are mathematical abstractions of soap films: they minimize the Riemannian volume locally around every point. Finding minimal algebraic hypersurfaces in \(R^n\) for each n is a long-standing open problem posed by Hsiang. In 2010 Tkachev gave a partial solution to this problem showing that the hypersurface of n x n real matrices of corank one is minimal. I will discuss the following generalization of this fact to all determinantal matrix varieties: for any m, n and r<m,n the (open) variety of m x n real matrices of rank r is minimal.