In this lecture we discuss how to complete a partially specied matrix to a positive semidenite matrix. This includes questions like deciding existence and constructing a completion, and determining the smallest possible rank of a completion. We present structural results and algorithms that take the graph of specied entries into account. This combinatorial approach leads to links between various areas: cut and metric polytopes in combinatorial op- timization, correlation matrices and distance matrices in distance geometry, Euclidean graph realizations and Colin de Verdière type geometric graph invariants
Monique Laurent is leader of the research group Algorithms, Combinatorics and Optimization at CWI in Amsterdam and professor at the University of Tilburg. She received her PhD degree in Mathematics at the University Paris Diderot in 1986. Before joining CWI in 1997, she has held positions at CNET and at CNRS in Paris. She was also a Humboldt fellow at the University of Bonn in 1991/92 and had visiting positions e.g. at Yale University, IASI-CNR in Rome, and Tokyo Institute of Technology. Her research field is combinatorial optimization with a focus on algorithmic methods using algebraic tools and semidefinite programming. She has more than 80 publications and co-authored the book `Geometry of Cuts and Metrics’. She is an editor of Mathematics of Operations Research, SIAM Journal on Optimization and SIAM Journal on Discrete Mathematics. She has been involved in national and international EU projects and in the organization of various scientific events, including workshops and seminars on Combinatorial Optimization, Semidefinite Programming, and on Algorithms for Real Algebraic Geometry in Oberwolfach, and a thematic semester program on Optimization at IPAM in Los Angeles.
More information is available at http://www.cwi.nl/ monique
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Vendredi 9 novembre - 14h30
PUIO (petit amphi)
Bât 640, Rue Joliot Curie / 91400 Orsay