Oberwolfach Reports

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Volume 11, Issue 2, 2014, pp. 1459–1513
DOI: 10.4171/OWR/2014/27

Published online: 2015-02-27

Okounkov Bodies and Applications

Megumi Harada[1], Kiumars Kaveh[2] and Askold Khovanskii[3]

(1) McMaster University, Hamilton, Canada
(2) University of Pittsburgh, USA
(3) University of Toronto, Toronto, Canada

The theory of Newton–Okounkov bodies, also called Okounkov bodies, is a relatively 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. Following a successful MFO Mini-workshop on this topic in August 2011, the MFO Half-Workshop 1422b, “Okounkov bodies and applications”, held in May 2014, explored the development of this area in recent years, with particular attention to applications and relationships to other areas such as number theory and tropical geometry.

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Harada Megumi, Kaveh Kiumars, Khovanskii Askold: Okounkov Bodies and Applications. Oberwolfach Rep. 11 (2014), 1459-1513. doi: 10.4171/OWR/2014/27