School of Mathematics, Statistics and Physics

Seminar Item

Pure Maths (Analysis) - Matina Trachana (Newcastle)

The matrix-valued moment problem for flat data

Date/Time: Monday 14 December 3.00pm - Analysis Seminar

Venue: Zoom

Abstract: In this talk we will consider the truncated matrix-valued moment problem on ​$\mathbb{R}^d.$ In terms of algebraic geometry, we will present a flat extension theorem for matricial moments via an appropriate analogue of the flat extension theorem of Curto and Fialkow in the scalar case given in 1996. In their work, the authors show that when the truncated moment problem is of flat data type, a solution exists and can be constructed from the simultaneous zeros of a collection of polynomials which describe the linear dependence of the extension of the moment matrix. Based on matrix positivity and extension, we will sketch a generalisation in the matricial setting and establish necessary and sufficient conditions for a minimal solution to the truncated matrix-valued moment problem. Moreover, we will showcase necessary and sufficient conditions for a minimal solution to the quadratic matrix-valued moment problem. This talk is based on joint work with Dr David Kimsey.