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Monthly Archives: January 2011
Notes of Jean Lasserre’s lecture nr 1
Moments, positive polynomials and optimization Hierarchies will come only at the very end, as a tool that helps solving basic problems with many applications. The main theorems will have two facets: real algebraic geometry (positive polynomials), and functional analysis … Continue reading
Notes of Nati Linial’s lecture nr 2
Last time, I went through fundamental results in extremal graph theory and explained the model. Today, I will go more into results of mine. But let me finish the proof of a theorem I quoted last time. 1. Back to … Continue reading
Abstract of Urs Lang’s course
Injective metric spaces, or absolute 1Lipschitz retracts, share a number of properties with CAT(0) spaces. In the 1960es, Isbell showed that every metric space possesses an essentially unique injective hull (envelope), and Cohen established the corresponding result in the linear … Continue reading
Notes of Guy Kindler’s lecture nr 1
Dictatorship testing and hardness of approximation We shall explain a few sharp hardness of approximation results. This involves several components: PCP, Parallel Repetition, discrete analysis. Then all these components must be merged together, and it is usually delicate. Several points … Continue reading
Slides of Claire Mathieu’s lecture nr 5
Claire wrote on the tablet ihpjan252011 and used part of the following slides clusteringGDR
Notes of Claire Mathieu’s lecture nr 5
Scribe: Eric Colin de VerdiÃ¨re Here is the plan for today: Duality in linear programming, duality in semidefinite programming, application to correlation clustering (work by Warren Schudy and Claire Mathieu, SODA’10). 1. Duality As an example, let us consider the … Continue reading
Notes of Alain Valette’s lecture nr 3
In the first and second lectures, I defined coarse embeddings and gave examples. Now I give more details. 1. Examples of spaces not embeddable into Hilbert spaces Definition 1 Let be a family of finite collected, regular graphs, … Continue reading