The G-Stable Rank for Tensors

Abstract: The rank of a matrix can be generalized to tensors. In fact, there are many different rank notions for tensors that all coincide for matrices, such as the tensor rank, border rank, subrank and slice rank (and asymptotic versions of each of these). In this talk I will discuss two notions of rank that are closely related to Geometric Invariant Theory, the non-commutative rank and the G-stable rank. The non-commutative rank can be used for giving lower bounds for tensor rank and border rank. The G-stable rank was recently used by my graduate student Zhi Jiang to improve the asymptotic upper bounds of Ellenberg and Gijswijt for the Cap Set Problem.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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