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On Minimality of Determinantal Varieties

  • Khazhgali Kozhasov (Technical University Braunschweig)
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Abstract

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.</p>

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seminar
3/17/20 2/21/22

Nonlinear Algebra Seminar Online (NASO)

MPI for Mathematics in the Sciences Live Stream

Katharina Matschke

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