# Polyhedral structures in Algebraic Geometry (PhD minicourse, first lecture)

##
Stefano Urbinati

created by risa on 17 Jan 2018

23 jan 2018
-- 11:00

Aula 211, Dip.Matematica, Università "Roma Tre", Roma

**Abstract.**

Timetable.

Tue January 23rd 2018 - 11:00-13:00, Room 211

Thu January 25th 2018 - 11:00-13:00, Room 211

Abstract.

Algebraic geometry studies the zero locus of polynomial equations
connecting the related algebraic and geometrical structures. In
several cases, nevertheless the theory is extremely precise and
elegant, it is hard to read in a simple way the information behind
such structures. A possible way of avoiding this problem is that of
associating to polynomials some polyhedral structures that immediately
give some of the information connected to the zero locus of the
polynomial. In relation to this strategy I will introduce
Newton-Okounkov bodies and Tropical Geometry, underlying the
connection between the two theories.
I will conclude stating a recent result in collaboration with E.
Postinghel, where the interplay of tropical geometry and
Newton-Okounkov bodies gives a flat degeneration for Mori Dream
Spaces.