Laboratory of Mathematical Logic at PDMI

Пятница, 19 февраля, Zoom. Начало в 18:00.

Докладчик: Vladimir Lysikov (University of Copenhagen).

Тема: Weighted slice rank of tensors.

Abstract

Structural and computational understanding of tensors and restrictions between tensors is the driving force behind faster matrix multiplication algorithms, the unraveling of quantum entanglement, and the breakthrough on the cap set problem in combinatorics.
We introduce weighted slice ranks, a new family of monotone functionals on tensors which generalizes the slice rank functional used in work on cap sets and barriers for matrix multiplication algorithms.
We connect weighted slice rank to quantum functionals of Christandl, Vrana and Zuiddam, showing a possible direction to generalize quantum functionals to tensors over fields of positive characteristic.
Additionally, we discuss connections of weighted slice ranks to rectangular matrix multiplication and tripartite-to-bipartite entanglement transformations.

The talk is based on joint works with M. Christandl (QMATH, U. Copenhagen), F. Le Gall (Nagoya U.) and J. Zuiddam (Courant Institute, NYU). References: arXiv:2012.14412, arXiv:2003.03019.

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