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:

**Scientific Committee**

Victor Buchstaber (Steklov Institute and Moscow State University), Yulij Ilyashenko (Cornell University, Independent University of Moscow and Higher School of Economics), Sergei Lando (Higher School of Economics, Moscow), Alexei Parshin (Steklov Institute, Moscow), Alexei Rudakov (Higher School of Economics and Institute for System Studies, Moscow), Frank Sottile (Texas A&M University)

**Organizing Committee**

Kiumars Kaveh (University of Pittsburgh), Valentina Kiritchenko (Higher School of Economics), Sergei Lando,*chairman* (Higher School of Economics, Moscow),
Evgenia Soprunova (Kent State University),
Ivan Soprunov (Cleveland State University),
Vladlen Timorin (Higher School of Economics)

**Sponsoring institutions**

- 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

Victor Buchstaber (Steklov Institute and Moscow State University), Yulij Ilyashenko (Cornell University, Independent University of Moscow and Higher School of Economics), Sergei Lando (Higher School of Economics, Moscow), Alexei Parshin (Steklov Institute, Moscow), Alexei Rudakov (Higher School of Economics and Institute for System Studies, Moscow), Frank Sottile (Texas A&M University)

Kiumars Kaveh (University of Pittsburgh), Valentina Kiritchenko (Higher School of Economics), Sergei Lando,