Пятница 19.02. Vladimir Lysikov (University of Copenhagen): "Weighted slice rank of tensors"
PDMI seminars
Тема: Weighted slice rank of tensors
Место: Zoom
Время: 19.02.2021, 17:00
Докладчик: Vladimir Lysikov (University of Copenhagen)
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.
Alexander V. Smal
https://us02web.zoom.us/j/8141238054?pwd=Q2RMak9XU2dQSFlZcm5xV3VzZzdPZz09
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Alexander V. Smal
St. Petersburg Department of Steklov Mathematical Institute
27 Fontanka, St. Petersburg, 191023, Russia
Alexander V. Smal
По просьбам участников начало доклада переносится на 18:00.
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