Yusuf Civan (University of Manchester)
mbbxfyc4@maths.man.ac.uk The aim of this talk is to provide an introduction to a fascinating relation among combinatorics, algebraic geometry and topology as it has developed last three decades by various mathematicians (Demazure, Danilov, Batyrev, etc.) This relation is known as the theory of toric varieties or sometimes as torus embeddings. Toric varieties provide a remarkable area to study algebro-geometric or topological problems in the language of combinatorial objects much like the simplicial complexes. I will present two different constructions of a toric variety; the first one is due to algebraic geometers in which it is formed by pieces, affine toric varieties, and the second one owes its existence to symplectic geometers (Audin), which is more compatible in a sense that it can be obtained as a quotient of a complex space by an action of an algebraic torus. I will also give a brief background on the combinatorial side, and provide some important examples which I have been working on.