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Recent Progress and Open Problems in Algorithmic Convex Geometry Vempala, Santosh S. convex geometry geometric inequalities algorithms sampling optimization integration rounding learning This article is a survey of developments in algorithmic convex geometry over the past decade. These include algorithms for sampling, optimization, integration, rounding and learning, as well as mathematical tools such as isoperimetric and concentration inequalities. Several open problems and conjectures are discussed on the way. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Santosh S. Vempala 2010 Is Part Of LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2010.42 urn:nbn:de:0030-drops-28529 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.42 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode