Asymptotic Spectrum and Approximation Approaches to Direct-sum Problems

Jeroen Zuiddam examines whether repeated tasks permit economies of scale, focusing on fast matrix multiplication and graph Shannon capacity as unresolved direct-sum problems. The talk introduces Strassen's asymptotic-spectrum duality, originally developed for asymptotic tensor rank and later applied to Shannon capacity and other problems. It then explores approximation by sequences of easier instances: suitable notions of convergence, construction of the sequences, asymptotic-spectrum distance, and approaches using polynomials and algebraic geometry. Based on joint work with David de Boer, Pjotr Buys, Sven Polak, Matthias Christandl, Koen Hoeberechts, Harold Nieuwboer, and Péter Vrana.