## Arithmetic Okounkov bodies I

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We will review the construction of Newton-Okounkov bodies by Kaveh-Khovanskii and Lazarsfeld-Mustata, within a general framework of semigroups and cones associated to filtrations.

## Arithmetic Okounkov bodies II

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We will address the construction of arithmetic Newton-Okounkov bodies, and more generally functions on Newton-Okounkov bodies arising from filtrations, following ideas of Boucksom and collaborators.

## Arithmetic Okounkov bodies III

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In the third talk we will continue the discussion of arithmetic Newton-Okounkov bodies and more.