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Tensor Computations: Applications and Optimization (Dagstuhl Seminar 22101) Bientinesi, Paolo Ham, David Huang, Furong Kelly, Paul H. J. Sadayappan, P. (Saday) Stow, Edward Tensor Optimisation Linear Algebra Compilers Benchmark Domain Specific Language This report documents the program and the outcomes of Dagstuhl Seminar 22101 "Tensor Computations: Applications and Optimization". Tensors are higher dimensional analogs of matrices, and represent a key data abstraction for many applications in computational science and data science. Widely used shared infrastructure exists for linear algebra, while, in contrast, for tensor computations, there is no consensus on standard building blocks. This Dagstuhl Seminar aimed to bring together users, and performance optimization specialists, to build such foundations. We present the abstracts of the 5 tutorials and 14 talks given. The working groups and their outcomes so far are then presented. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Paolo Bientinesi and David Ham and Furong Huang and Paul H. J. Kelly and P. (Saday) Sadayappan and Edward Stow 2022 Is Part Of Dagstuhl Reports, Volume 12, Issue 3 (2022) Article Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagRep.12.3.1 urn:nbn:de:0030-drops-172674 https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.3.1 eng https://creativecommons.org/licenses/by/4.0/legalcode