Combinatorial and birational aspects of algebraic geometry

This project will look at the interactions between algebra and geometry. The initial focus will be on algebraic geometry, and its deep links with combinatorics and complex geometry. This might include an investigation of toric varieties and Fano varieties. Both toric varieties and Fano varieties play crucial role in algebraic geometry, and also provide rich field of examples for number theory, mathematical physics and differential geometry.

The project will be devoted to the study of links between geometry and algebra intrinsic to algebraic geometry in the case of toric varieties, or the birational geometry of Fano varieties.