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The theory of Newton-Okounkov bodies, also called Okounkov bodies, is a new connection between algebraic geometry and convex geometry. It generalizes the well-known and extremely rich correspondence between geometry of toric varieties and combinatorics of convex integral polytopes. Okounkov bodies were first introduced by Andrei Okounkov, in a construction motivated by a question of Khovanskii concerning convex bodies govering the multiplicities of representations. Recently, Kaveh-Khovanskii and Lazarsfeld-Mustata have generalized and systematically developed Okounkov’s construction, showing the existence of convex bodies which capture much of the asymptotic information about the geometry of () where is an algebraic variety and is a big divisor. The study of Okounkov bodies is a new research area with many open questions. The goal of this mini-workshop was to bring together a core group of algebraic/symplectic geometers currently working on this topic to establish the groundwork for future development of this area.
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Megumi Harada, Kiumars Kaveh, Askold Khovanskii, Mini-Workshop: New Developments in Newton-Okounkov Bodies. Oberwolfach Rep. 8 (2011), no. 3, pp. 2327–2363DOI 10.4171/OWR/2011/41