Events for 11/04/2021 from all calendars

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: E. Gnang, Johns Hopkins University

Title: A Hypermatrix Analog of the General Linear Group

Abstract: Matrices are so ubiquitous and so deeply ingrained into our mathematical lexicon that one naturally asks: “Are there higher-dimensional analogs of matrices; more importantly why bother with them at all?” In short, hypermatrices are higher-dimensional matrices. Hypermatrices are important because they broaden the scope of matrix concepts such as spectra and group actions. Hypermatrix algebras also illuminate subtle aspects of matrix algebra. In this talk we describe an instance where the transition from matrices to third order hypermatrices results in a symmetry breaking of two equivalent definitions of the matrix general linear group. We show how this transition shines a light on subtle details of invariant theory.