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Seminar

Fellowship of the Ring: Tensor Ranks and Matrix Multiplication Complexity March 29, 2022 (01:00 PM PDT - 02:30 PM PDT)
Parent Program: --
Location: MSRI: Online/Virtual
Speaker(s) Hang Huang (University of Wisconsin-Madison)
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Video

Fellowship Of The Ring: Tensor Ranks And Matrix Multiplication Complexity

Abstract/Media

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Tensors are just multi-dimensional arrays. Notions of ranks and border rank abound in the literature. Tensor decompositions also have a lot of application in data analysis, physics, and other areas of science. I will survey my recent two results about tensor ranks and their application to matrix multiplication complexity. The first result relates different notion of tensor ranks to polynomials of vanishing Hessian. The second one computes the border rank of 3 X 3 permanent, which is important in the theory of matrix multiplication complexity. I will also briefly discuss the newest technique we used to achieve our results: border apolarity. Furthermore, I will survey on how this new technology helps us to compute/bound border rank of a lot of tensors of interests that were considered to be inaccessible before.

92947?type=thumb Tensor Ranks and Matrix Multiplication Complexity 437 KB application/pdf

Fellowship Of The Ring: Tensor Ranks And Matrix Multiplication Complexity