Events for 04/15/2019 from all calendars

Geometry Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Jurij Volcic, TAMU

Title: Free loci of noncommutative polynomials

Abstract: Let f be a noncommutative polynomial. The free locus of f is the set of all tuples of matrices X such that f(X) is singular. That, is the free locus is an infinite family of determinantal hypersurfaces (one for each size of matrices). The adjective ``free'' relates to quickly emerging free analysis and free real algebraic geometry, which study noncommutative functions on matrices in a certain dimension-free setting. Free loci play are important in (noncommutative) control theory and convex optimization. However, in this talk we will connect them to factorization in free algebra: roughly speaking, components of the free locus of f correspond to distinct irreducible factors of f, and irreducible polynomials are determined by their free loci. We will focus on the role of invariant theory for the general (and special) linear group in the proof. The talk is based on joint work with Bill Helton and Igor Klep.