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When we see someone performing at the top of their craft, we often marvel at both their observable achievements and the hidden internal expertise that they’ve accumulated. Something similar is true, in a very different way, with generative AI and large...
A classical result of Strassen connects the exponent $\omega$ of square matrix multiplication to the exponent (asymptotic rank) of the $2\times 2$ matrix multiplication tensor. This talk looks at a collection of recent results that connect exponents of other constant-size tensors to the study of algorithms for a range of hard problems such as the set cover problem, the graph coloring problem, and the matrix permanent problem. We highlight the sequence of balanced tripartitioning tensors as a particular sequence of interest in connection with the matrix permanent problem.
Based on joint work with Andreas Björklund (Lund), Radu Curticapean (Copenhagen & Regensburg), Thore Husfeldt (Copenhagen), Tomohiro Koana (Kyoto), Mateusz Michałek (Konstanz), Jesper Nederlof (Utrecht), and Kevin Pratt (New York).