Complexity and geometry of bilinear maps
This is the written exposition of a talk for a general mathematical audience, held by the author at the DMV-meeting. Complexity and degeneration of bilinear maps may be described by a single data structure: the asymptotic spectrum. The paper gives an introduction to this theory. As a red thread it uses \(\omega\), the exponent of matrix multiplication. The paper has been supplemented by footnotes containing more details and by an appendix, which is an invitation to application-oriented algebraists and geometers to be become acquainted with the topic. It contains short new proofs for some results in the main text, conjectures, and relations to other topics.
scientific article; zbMATH DE number 2182695