On Minimality of Determinantal Varieties

Abstract: Minimal submanifolds are mathematical abstractions of soap films: they minimize the Riemannian volume locally around every point. Finding minimal algebraic hypersurfaces in 𝑅𝑛 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

commutative algebraalgebraic geometry

Audience: researchers in the topic

Max Planck Institute nonlinear algebra seminar online

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