Speaker: Joaquim Roé (UAB)

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. In a second talk 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. If time permits, links with diophantine approximation and Donaldson stability theory in Kähler geometry will also be covered.

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