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Positive semidefinite lifts and factorizations

Introductory Workshop: Geometric and Topological Combinatorics September 05, 2017 - September 08, 2017

September 08, 2017 (10:30 AM PDT - 11:30 AM PDT)
Speaker(s): João Gouveia (University of Coimbra)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

Representing polytopes by means of linear matrix inequalities as been a highly successful strategy in combinatorial optimization. Geometrically it corresponds to writing a polytope as the projection of an affine slice of the cone of positive semidefinite (psd) matrices i.e., a spectrahedron. Efforts to understand the theoretical limits of such techniques have connected the existance of such representations to a particular type of matrix factorization, the psd factorization of a nonnegative matrix, and its corresponding notion of psd rank. In this talk we will do a brief survey of the main results in the area, its connections to matrix theory and combinatorics and some of the open problems that remain.

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Video/Audio Files

16-Gouveia

H.264 Video 16-Gouveia.mp4 118 MB video/mp4 rtsp://videos.msri.org/data/000/029/368/original/16-Gouveia.mp4 Download
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