Toric geometry exhibited a profound relation between algebra and topology on one side and combinatorics and convex geometry on the other side. In the last decades, the interplay between algebraic and convex geometry has been explored and used successfully in a much more general setting: first, for varieties with an algebraic group action (such as spherical varieties) and recently for all algebraic varieties (construction of Newton–Okounkov bodies). The main goal of the conference is to survey recent developments in these directions. The conference is not intended to focus on a narrow set of problems, but rather to present a broad look at recent progress in the field, highlighting new techniques and ideas. Main topics of the conference are:

• Theory of Newton polytopes and Newton–Okounkov bodies
• Toric geometry, geometry of spherical varieties, Schubert calculus, geometry of moduli spaces
• Tropical geometry and convex geometry
• Real algebraic geometry, fewnomial theory and o-minimal structures
• Polynomial vector fields and the Hilbert 16th problem

The conference is dedicated to Askold Georgievich Khovanskii, who will turn sixty five in June 2012. Askold Khovanskii put his indelible mark on many areas of mathematics: real and complex algebraic geometry, singularity theory, differential equations, topology. He obtained many major results (both alone and with his collaborators) in all areas covered by the conference.

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Website: https://bogomolov-lab.ru/AG2012/Askoldfest2012.htm